Download App

Relations and Functions — Maths STD 12 Science — Question

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Relations and Functions→Relations and Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $ a,b,c $ are three coplanar vectors, then $[a + b\,\,b + c\,\,c + a] = $
→
Let $\text{f(x)}=\begin{vmatrix}\cos\text{x}&\text{x}&1\\2\sin\text{x}&\text{x}&2\text{x}\\\sin\text{x}&\text{x}&\text{x}\end{vmatrix},$ then $\lim_\limits{\text{x}\rightarrow0}\frac{\text{f(x)}}{\text{x}^2}$ is equal to:
→
$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $
→
$\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}}\frac{1}{1+\sqrt{\cot\text{x}}}\text{ dx}$ is:
→
The function $f(x)=\frac{x}{\log x}$ increases in the interval
→
Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}} .$ If $\overrightarrow{\mathrm{c}}$ is a vector such that $\vec{a} \times \vec{c}=\vec{b}$ and $\vec{a} \cdot \vec{c}=3$, then $\vec{a} \cdot(\vec{b} \times \vec{c})$ is equal to :
→
The number of discontinuous functions $y(x)$ on $[-2,2]$ satisfying $x^2+y^2=4$ is
→
Let $\overrightarrow{ a }=\hat{ i }+2 \hat{ j }-\hat{ k }, \overrightarrow{ b }=\hat{ i }-\hat{ j }$ and $\overrightarrow{ c }=\hat{ i }-\hat{ j }-\hat{ k }$ be three given vectors. If $\overrightarrow{ r }$ is a vector such that $\overrightarrow{ r } \times \overrightarrow{ a }=\overrightarrow{ c } \times \overrightarrow{ a }$ and $\overrightarrow{ r } \cdot \overrightarrow{ b }=0,$ then $\overrightarrow{ r } \cdot \overrightarrow{ a } \quad$ is equal to ...........
→
If $\int_{}^{} {\frac{{dx}}{{1 + \sin x}} = \tan \left( {\frac{x}{2} + a} \right) + b} $, then
→
If a relation $R$ on the set $\{1,2,3\}$ be defined by $R=\{(1,2)\}$, then $R$ is
→