If f(x) = ^2 x and the composite function g f(x) = | x|, then the… - Vidyadip

MCQ

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

A
$\sqrt {x - 1} $
✓
$\sqrt x $
C
$\sqrt {x + 1} $
D
$ - \sqrt x $

✓

Answer

Correct option: B.

$\sqrt x $

b
(b) $(gof)(x) = \,|\sin x|$ and $f(x) = {\sin ^2}x$

==> $g({\sin ^2}x) = \,|\sin x|$;

$\therefore$ $g(x) = \sqrt x $.

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