Question

If f(x) = $\left\{ \begin{aligned} & x^{2} for \rightleftharpoons x \geq 0 \\ & x for \rightleftharpoons x < 0 \end{aligned} \right.\$, then fof(x) is given by

• A. x² for x ≥ 0, x for x < 0
• B. x⁴ for x ≥ 0, x² for x < 0
• C. x⁴ for x ≥ 0, -x² for x < 0
• D. x⁴ for x ≥ 0, x for x < 0

Answer 1

Answer: (D)

x⁴ for x ≥ 0, x for x < 0

Answer 2

fof(x) = $\left\{ \begin{aligned} & f^{2}(x) for\mspace{6mu} f(x) \geq 0 \\ & f(x) for\mspace{6mu} f(x) < 0 \end{aligned} \right.\$ = $\left\{ \begin{aligned} & x^{4} x \geq 0 \\ & x x < 0 \end{aligned} \right.\$