ข้อสอบ PAT 1 - มีนาคม 2560

$$\begin{gathered} \mathrm{จากโจทย์} f\left(n\right)=\left\{\begin{array}{ll}\left(f\circ f\right)\left(n-4\right)& ,n>60 \to \boxed{1}\\ n+3& ,n\le 60 \to \boxed{2}\end{array}\right. \\ \underline{\mathrm{หาค่า} f\left(60\right)} ;60\le 60 \mathrm{จะได้กรณี} \boxed{2} \\ \mathrm{จาก} \boxed{2} \mathrm{จะได้} f\left(60\right) = 60+3 = 63 \end{gathered}$$

$$\begin{gathered} \underline{\mathrm{หาค่า} f\left(f\left(60\right)\right)} \\ f\left(f\left(60\right)\right) = f\left(63\right) ; 63>60 \mathrm{จะได้กรณี} \boxed{1} \\ \mathrm{จาก} \boxed{1} \mathrm{จะได้} f\left(63\right) = \left(f\circ f\right)\left(63-4\right) \\ = \left(f\circ f\right)\left(59\right) \\ = f\left(f\left(59\right)\right) ; 59\le 60 \mathrm{จะได้กรณี} \boxed{2} \\ \mathrm{จาก} \boxed{2} \mathrm{จะได้} = f\left(59+3\right) \\ = f\left(62\right) ; 62>60 \mathrm{จะได้กรณี} \boxed{1} \end{gathered}$$

$$\begin{gathered} \mathrm{จาก} \boxed{1} \mathrm{จะได้} = \left(f\circ f\right)\left(62-4\right) \\ = f\left(f\left(58\right)\right) ; 58\le 60 \mathrm{จะได้กรณี} \boxed{2} \\ \mathrm{จาก} \boxed{2} \mathrm{จะได้} = f\left(58+3\right) \\ = f\left(61\right) ; 61>60 \mathrm{จะได้กรณี} \boxed{1} \\ \mathrm{จาก} \boxed{1} \mathrm{จะได้} = \left(f\circ f\right)\left(61-4\right) \\ = f\left(f\left(57\right)\right) ; 57\le 60 \mathrm{จะได้กรณี} \boxed{2} \\ \mathrm{จาก} \boxed{2} \mathrm{จะได้} = f\left(57+3\right) \\ = f\left(60\right) \end{gathered}$$

$$\begin{gathered} \mathrm{ดังนั้น} f\left(63\right) = f\left(62\right) = f\left(61\right) = f\left(60\right) = 63 \\ \mathrm{หาค่าของ} f\left(f\left(f\left(60\right)\right)\right) = f\left(f\left(63\right)\right) ; f\left(63\right)=63 \\ = f\left(63\right) \\ = 63 \end{gathered}$$​