First slide

Functions (XII)

Question

If $f (x) = \sin^{2} x$ and the composite functions $g (f (x)) = | \sin x |$ then g(x) is equal to

Moderate

A

$\sqrt{x - 1}$
B

$\sqrt{x}$
C

$\sqrt{x + 1}$
D

$- \sqrt{x}$

Solution

We have,
$f (x) = \sin^{2} x and g (f (x)) = | \sin x |$
Now,
$\begin{aligned} g (f (x)) = | \sin x | \\ \Rightarrow & g (f (x)) = \sqrt{\sin^{2} x} \Rightarrow g (\sin^{2} x) = \sqrt{\sin^{2} x} \\ ∴ & g (x) = \sqrt{x} \end{aligned}$

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