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STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
If $g(f(x)) = |\sin x|$ and $f(g(x)) = (\sin \sqrt x )^2$, then
  • ✓
    $ƒ(x) = \sin^2x, g(x) = \sqrt x$
  • B
    $ƒ(x) = \sin x, g(x) = |x|$
  • C
    $ƒ(x) = x^2, g(x) = \sin \sqrt x$
  • D
    $ƒ$ and $g$ can not be found
✓

Answer

Correct option: A.
$ƒ(x) = \sin^2x, g(x) = \sqrt x$
a
$g o f=g\{f(x)\}=|\sin x|=\sqrt{\sin ^{2} x}$

Also, $f o g=f\{g(x)\}=\sin ^{2} \sqrt{x}$

Obviously, $\sqrt{\sin ^{2} x}=\sqrt{f(x)}$

and $\sin ^{2} \sqrt{x}=\sin ^{2}\{g(x)\}$

i.e., $f(x)=\sin ^{2} x$

and $g(x)=\sqrt{x}$

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