First slide

Functions (XII)

Question

If $f (x) = \{\begin{cases} x^{2}, for x \geq 0 \\ x, for x < 0 \end{cases}$ , then $f o f (x)$ is given by

Moderate

A

$x^{2} for x \geq 0, x for x < 0$
B

$x^{4} for x \geq 0, x^{2} for x < 0$
C

$x^{4} for x \geq 0, - x for x < 0$
D

$x^{4} for x \geq 0, x for x < 0$

Solution

$\begin{array}{l} f (f (x)) = \{\begin{cases} {(f (x))}^{2}, for f (x) \geq 0 \\ f (x), for f (x) < 0 \end{cases} \\ = \{\begin{cases} {(x^{2})}^{2}, x^{2} \geq 0, x \geq 0 \\ x^{2}, x \geq 0, x < 0 \\ x^{2}, x^{2} < 0, x \geq 0 \\ x, x < 0, x < 0 \end{cases} \\ = \{\begin{cases} x^{4}, x \geq 0 \\ x, x < 0 \end{cases} \end{array}$

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