ข้อสอบ PAT 1 - มีนาคม 2556

ข้อ 7

ให้ R แทนเซตของจำนวนจริง พิจารณาข้อความต่อไปนี้

(ก) ความสัมพันธ์ begin mathsize 12px style space space space space space space space space space space space space space space space space space space 8 to the power of 10 over 2 open square brackets 2 a subscript 1 plus open parentheses 10 minus 1 close parentheses open parentheses 1 third close parentheses close square brackets end exponent space space equals space 2 to the power of 15
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 8 to the power of 10 a subscript 1 plus 15 end exponent space space equals space space 2 to the power of 15
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 8 to the power of 10 a subscript 1 plus 15 end exponent space space equals space space open parentheses 2 close parentheses to the power of 15
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 open parentheses 2 close parentheses to the power of 3 open parentheses 10 a subscript 1 plus 15 close parentheses end exponent space space equals space space open parentheses 2 close parentheses to the power of 15
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 30 a subscript 1 plus 45 space space equals space space 15
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 space space space space a subscript 1 space space equals space space minus 1 end style เป็นฟังก์ชัน

(ข) ถ้า begin mathsize 12px style space space space space space space space space space space space space space space space space space space 8 to the power of 10 over 2 open square brackets 2 a subscript 1 plus open parentheses 10 minus 1 close parentheses open parentheses 1 third close parentheses close square brackets end exponent space space equals space 2 to the power of 15
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 8 to the power of 10 a subscript 1 plus 15 end exponent space space equals space space 2 to the power of 15
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 8 to the power of 10 a subscript 1 plus 15 end exponent space space equals space space open parentheses 2 close parentheses to the power of 15
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 open parentheses 2 close parentheses to the power of 3 open parentheses 10 a subscript 1 plus 15 close parentheses end exponent space space equals space space open parentheses 2 close parentheses to the power of 15
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 30 a subscript 1 plus 45 space space equals space space 15
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 space space space space a subscript 1 space space equals space space minus 1 end style และ begin mathsize 16px style g open parentheses 3 x minus 1 close parentheses equals 2 x squared plus 3 x end style สำหรับ begin mathsize 16px style x element of R end style แล้วค่าของ begin mathsize 16px style open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses 25 close parentheses equals 14 end style

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