First slide

Functions (XII)

Question

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

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

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

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

Solution

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

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