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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
If $\text{g(f(x))}=|\sin\text{x}|$ and $\text{f(g(x))}=(\sin\sqrt{\text{x}})^2,$ then
  • ✓
    $\text{f(x)}=\sin^2\text{x},\ \text{g(x)}=\sqrt{\text{x}}$
  • B
    $\text{f(x)}=\sin\text{x},\ \text{g(x)}=|\text{x}|$
  • C
    $\text{f(x)}=\text{x}^2,\ \text{g(x)}=\sin\sqrt{\text{x}}$
  • D
    $f$ and $g$ can not be determined.
✓

Answer

Correct option: A.
$\text{f(x)}=\sin^2\text{x},\ \text{g(x)}=\sqrt{\text{x}}$
If we solve it by the trial$-$and$-$error method, we can see that $(a)$ satisfies the given condition.
From $(a):$
$\text{f(x)}=\sin^2\text{x}$ and $\text{g(x)}=\sqrt{\text{x}}$
$\Rightarrow\ \text{f(g(x))}=\text{f}(\sqrt{\text{x}})=\sin^2\sqrt{\text{x}}$
$=(\sin\sqrt{\text{x}})^2$

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