ข้อสอบ PAT 1 - กุมภาพันธ์ 2563

$$\begin{gathered} \mathrm{หา} R_f \mathrm{โดยการพิจารณาช่วงค่าที่เป็นไปได้} \\ x^2 \ge 0 \\ 0 \ge -x^2 \\ 5 \ge 5-x^2 \\ 5 \ge f\left(x\right) \to R_f = (-\infty , 5] \end{gathered}$$

$$\begin{gathered} \mathrm{แทนค่า} f \mathrm{และ} R_f \mathrm{ใน} g\left(x\right) \\ \mathrm{จะได้} g\left(x\right) = \left\{\begin{array}{ll}5-{\left(x+1\right)}^2& ; x \in (-\infty ,5]\\ 1& ; x \notin (-\infty ,5]\end{array}\right. \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} \left(f\circ g\right)\left(6\right)-\left(g\circ f\right)\left(3\right) = f\left(g\left(6\right)\right)-g\left(f\left(3\right)\right) \\ = f\left(1\right)-g\left(5-3^2\right) \\ = f\left(1\right)-g\left(-4\right) \\ = \left(5-1^2\right)-\left[5-\left(-4+1^2\right)\right] \\ = 4-\left(-4\right) = 8 \end{gathered}$$