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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
MCQ
If $f(x) = (ax^2 + b)^3,$ then the function $g$ such that $f(g(x)) = g(f(x))$ is given by:
  • A
    $\text{g}(\text{x})=\Big(\frac{\text{b}-\text{x}^\frac{1}{3}}{\text{a}}\Big)$
  • B
    $\text{g}(\text{x})=\frac{1}{(\text{ax}^2+\text{b})^3}$
  • C
    $\text{g}(\text{x})=(\text{ax}^2+\text{b})^\frac{1}{3}$
  • ✓
    $\text{g}(\text{x})=\Big(\frac{\text{x}^\frac{1}{3}-\text{b}}{\text{a}}\Big)^\frac{1}{2}$
✓

Answer

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

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