Q. If $f(x) = \sin^{2}x$ and the composite function $g\left( f(x) \right) = |\sin x|$, then the function $g(x)$ is equal to
A) $\sqrt{x - 1}$
B) $\sqrt{x}$
C) $\sqrt{x + 1}$
D) $- \sqrt{x}$
Explanation
(b)
Since, $g\left( f(x) \right) = \left| \sin x \right|$
$\Rightarrow \ \ \ \ \ g\left( \sin^{2}x \right) = {|sin}{x|}$
$\Rightarrow \ \ \ \ \ \ \ g\left( \sin^{2}x \right) = \sqrt{\sin^{2}x}\ \ \ \ \ \ \therefore\ \ \ \ g(x) = \sqrt{x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.