ข้อสอบ PAT 1 - มีนาคม 2559

ข้อ 17

ให้ f เป็นฟังก์ชัน โดยที่
 f open parentheses x close parentheses equals open curly brackets table row cell x plus b minus 4 end cell row cell x squared plus b x plus a end cell row cell 2 b x minus a end cell end table close space space table row comma row comma row comma end table space space space table row cell space space space x less or equal than a end cell row cell a less than x less or equal than b end cell row cell x greater than b end cell end table space space space space space

เมื่อ a และ b เป็นจำนวนจริง
และ f เป็นฟังก์ชันต่อเนื่องบนเซตของจำนวนจริง พิจารณาข้อความต่อไปนี้

     (ก) open parentheses f ring operator f close parentheses open parentheses a minus b close parentheses space equals space a minus b

     (ข) f open parentheses a plus b close parentheses space equals space f open parentheses a close parentheses plus f open parentheses b close parentheses

     (ค) f apostrophe open parentheses f open parentheses 2 close parentheses close parentheses space equals space f open parentheses f apostrophe open parentheses 2 close parentheses close parentheses

ข้อใดต่อไปนี้ถูกต้อง

รีวิว - เสียงตอบรับจากผู้เรียน
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด
รีวิวสอบติด

เฉลยข้อสอบ

begin mathsize 12px style จากโจทย ์ space space space space space f open parentheses x close parentheses space equals space open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x plus b minus 4 comma end cell cell x italic less or equal than italic space a space rightwards arrow box enclose 1 end cell row cell x squared plus b x plus a comma end cell cell a less than x less or equal than b space rightwards arrow box enclose 2 end cell row cell 2 b x minus a comma end cell cell x greater than b space rightwards arrow space box enclose 3 end cell end table close f space เป ็ นฟ ั งช ั นก ์ ต ่ อเน ื่ องบนเซตของจำนวนจร ิ ง end style

begin mathsize 12px style bold minus bold โดย bold space bold italic f bold space bold ต ่ อเน ื่ องท ี่ bold space bold italic x bold equals bold italic b จะได ้ space space space space space space space space space space space space f open parentheses b close parentheses space equals space limit as x rightwards arrow b of f open parentheses x close parentheses bold โดย space limit as x rightwards arrow b of f open parentheses x close parentheses equals limit as x rightwards arrow b to the power of plus of f open parentheses x close parentheses equals limit as x rightwards arrow b to the power of minus of f open parentheses x close parentheses space space end style

begin mathsize 12px style จากโจทย ์ space space space space space 3 to the power of 2 x plus 10 end exponent minus 4 open parentheses 3 to the power of x plus 6 end exponent close parentheses plus 27 space less or equal than space 0 จะได ้ space space space space space space space space space 3 to the power of 2 open parentheses x plus 5 close parentheses end exponent minus 4 times 3 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space open parentheses 3 to the power of open parentheses x plus 5 close parentheses end exponent close parentheses squared minus 12 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 กำหนดให ้ space space space space space A space equals space 3 to the power of x plus 5 end exponent จะได ้ space space space space space space space space space space space space A squared minus 12 A plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space open parentheses A minus 9 close parentheses open parentheses A minus 3 close parentheses space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A less or equal than 9 space comma space 3 end style


begin mathsize 12px style จะได ้ space space space space space space space space space space space space 3 space less or equal than space A space less or equal than space 9 space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x plus 5 end exponent space less or equal than space 3 squared space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x times 3 to the power of 5 space less or equal than space 3 squared space space space space space space space space space space space space space space space space fraction numerator space 3 to the power of 1 over denominator 3 to the power of 5 end fraction space less or equal than space 3 to the power of x space less or equal than space 3 squared over 3 to the power of 5 space space space space space space space space space space space space space space space space 3 to the power of negative 4 end exponent space less or equal than space space 3 to the power of x space less or equal than space space 3 to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space minus 4 space less or equal than space x space less or equal than space minus 3 ด ั งน ั้ น space space space space space space space A equals left square bracket negative 4 comma negative 3 right square bracket space subset of space left parenthesis negative 5 comma negative 2 right parenthesis bold ด ั งน ั้ น bold space bold ตอบ bold space bold 2 bold right parenthesis bold space bold space bold left parenthesis bold minus bold 5 bold comma bold minus bold 2 bold right parenthesis end style

begin mathsize 12px style จากโจทย ์ space space space space space 3 to the power of 2 x plus 10 end exponent minus 4 open parentheses 3 to the power of x plus 6 end exponent close parentheses plus 27 space less or equal than space 0 จะได ้ space space space space space space space space space 3 to the power of 2 open parentheses x plus 5 close parentheses end exponent minus 4 times 3 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space open parentheses 3 to the power of open parentheses x plus 5 close parentheses end exponent close parentheses squared minus 12 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 กำหนดให ้ space space space space space A space equals space 3 to the power of x plus 5 end exponent จะได ้ space space space space space space space space space space space space A squared minus 12 A plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space open parentheses A minus 9 close parentheses open parentheses A minus 3 close parentheses space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A less or equal than 9 space comma space 3 end style

begin mathsize 12px style จะได ้ space space space space space space space space space space space space 3 space less or equal than space A space less or equal than space 9 space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x plus 5 end exponent space less or equal than space 3 squared space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x times 3 to the power of 5 space less or equal than space 3 squared space space space space space space space space space space space space space space space space fraction numerator space 3 to the power of 1 over denominator 3 to the power of 5 end fraction space less or equal than space 3 to the power of x space less or equal than space 3 squared over 3 to the power of 5 space space space space space space space space space space space space space space space space 3 to the power of negative 4 end exponent space less or equal than space space 3 to the power of x space less or equal than space space 3 to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space minus 4 space less or equal than space x space less or equal than space minus 3 ด ั งน ั้ น space space space space space space space A equals left square bracket negative 4 comma negative 3 right square bracket space subset of space left parenthesis negative 5 comma negative 2 right parenthesis bold ด ั งน ั้ น bold space bold ตอบ bold space bold 2 bold right parenthesis bold space bold space bold left parenthesis bold minus bold 5 bold comma bold minus bold 2 bold right parenthesis end style

begin mathsize 12px style จากโจทย ์ space space space space space 3 to the power of 2 x plus 10 end exponent minus 4 open parentheses 3 to the power of x plus 6 end exponent close parentheses plus 27 space less or equal than space 0 จะได ้ space space space space space space space space space 3 to the power of 2 open parentheses x plus 5 close parentheses end exponent minus 4 times 3 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space open parentheses 3 to the power of open parentheses x plus 5 close parentheses end exponent close parentheses squared minus 12 open parentheses 3 to the power of x plus 5 end exponent close parentheses plus 27 space less or equal than space 0 กำหนดให ้ space space space space space A space equals space 3 to the power of x plus 5 end exponent จะได ้ space space space space space space space space space space space space A squared minus 12 A plus 27 space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space open parentheses A minus 9 close parentheses open parentheses A minus 3 close parentheses space less or equal than space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A less or equal than 9 space comma space 3 end style

begin mathsize 12px style จะได ้ space space space space space space space space space space space space 3 space less or equal than space A space less or equal than space 9 space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x plus 5 end exponent space less or equal than space 3 squared space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x times 3 to the power of 5 space less or equal than space 3 squared space space space space space space space space space space space space space space space space fraction numerator space 3 to the power of 1 over denominator 3 to the power of 5 end fraction space less or equal than space 3 to the power of x space less or equal than space 3 squared over 3 to the power of 5 space space space space space space space space space space space space space space space space 3 to the power of negative 4 end exponent space less or equal than space space 3 to the power of x space less or equal than space space 3 to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space minus 4 space less or equal than space x space less or equal than space minus 3 ด ั งน ั้ น space space space space space space space A equals left square bracket negative 4 comma negative 3 right square bracket space subset of space left parenthesis negative 5 comma negative 2 right parenthesis bold ด ั งน ั้ น bold space bold ตอบ bold space bold 2 bold right parenthesis bold space bold space bold left parenthesis bold minus bold 5 bold comma bold minus bold 2 bold right parenthesis end style

begin mathsize 12px style จะได ้ space space space space space space space space space space space space 3 space less or equal than space A space less or equal than space 9 space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x plus 5 end exponent space less or equal than space 3 squared space space space space space space space space space space space space space space space space space 3 to the power of 1 space less or equal than space 3 to the power of x times 3 to the power of 5 space less or equal than space 3 squared space space space space space space space space space space space space space space space space fraction numerator space 3 to the power of 1 over denominator 3 to the power of 5 end fraction space less or equal than space 3 to the power of x space less or equal than space 3 squared over 3 to the power of 5 space space space space space space space space space space space space space space space space 3 to the power of negative 4 end exponent space less or equal than space space 3 to the power of x space less or equal than space space 3 to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space minus 4 space less or equal than space x space less or equal than space minus 3 ด ั งน ั้ น space space space space space space space A equals left square bracket negative 4 comma negative 3 right square bracket space subset of space left parenthesis negative 5 comma negative 2 right parenthesis bold ด ั งน ั้ น bold space bold ตอบ bold space bold 2 bold right parenthesis bold space bold space bold left parenthesis bold minus bold 5 bold comma bold minus bold 2 bold right parenthesis end style

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