First slide

Functions (XII)

Question

If $f (x) = \frac{1}{x}, g (x) = \frac{1}{x^{2}}, and h (x) = x^{2},$ then

Easy

A

$f o g (x) = x^{2}, x \neq 0, h (g (x)) = \frac{1}{x^{2}}$
B

$h (g (x)) = \frac{1}{x^{2}}, x \neq 0, f o g (x) = x^{2}$
C

$f o g (x) = x^{2}, x \neq 0, h (g (x)) = {(g (x))}^{2}, x \neq 0$
D

none of these

Solution

$\begin{array}{l} f (x) = \frac{1}{x}, g (x) = \frac{1}{x^{2}}, and h (x) = x^{2} \\ f (g (x)) = x^{2}, x \neq 0 \\ h (g (x)) = \frac{1}{x^{4}} = {(g (x))}^{2}, x \neq 0 \end{array}$

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