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Relations and Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations and Functions1 Mark
MCQ
If $f(x)=\left(a x^2-b\right)^3$, then the function $g$ such that $f\{g(x)\}=g\{f(x)\}$ is given by:
  • A
    $\text{g(x)}=\Big(\frac{\text{b}-\text{x}^\frac{1}{3}}{\text{a}}\Big)^\frac{1}{2}$
  • B
    $\text{g(x)}=\frac{1}{(\text{ax}^2+\text{b})^3}$
  • C
    $\text{g(x)}=(\text{ax}^2+\text{b})^\frac{1}{3}$
  • ✓
    $\text{g(x)}=\Big(\frac{\text{x}^\frac{1}{3}+\text{b}}{\text{a}}\Big)^\frac{1}{2}$
✓

Answer

Correct option: D.
$\text{g(x)}=\Big(\frac{\text{x}^\frac{1}{3}+\text{b}}{\text{a}}\Big)^\frac{1}{2}$

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