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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES5 Marks
Question
If the function $\text{f: R}\rightarrow\text{R}$ be defined by $\text{f(x) = 2x - 3 and g : R}\rightarrow\text{R by g(x) = x}^{3} + 5,$ then find the value of $\text{(fog)}^{-1}(\text{x}).$
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Answer

$\text{Let y = (fog) (x) [say y = h (x)]}$
$ = \text{f[g (x)] = f(x}^{3} + 5)$
$= 2\text{(x}^{3} + 5) - 3$
$= 2 \text{x}^{3} + 7$
$\therefore\text{x} = \sqrt[3]\frac{\text{x - 7}}{2}= \text{h}^{-1}\text{(y)}$
$ \therefore\text{(fog)}^{-1} = \sqrt[3]\frac{\text{x - 7}}{2}$

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