If $f\left( x \right) = {\left( {2x - 3\pi } \right)^5} + \frac{4}{3}x + \cos x$ and $g$ is the inverse of $f$, then $g'\left( {2\pi } \right)$ = ?
If $f\left( x \right) = {\left( {2x - 3\pi } \right)^5} + \frac{4}{3}x + \cos x$ and $g$ is the inverse of $f$, then $g'\left( {2\pi } \right)$ = ?
- A
$\frac{7}{3}$
- B
$\frac{3}{7}$
- C
$\frac{{30{\pi ^4} + 4}}{3}$
- D
$\frac{3}{{30{\pi ^4} + 4}}$
Similar Questions
Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$, $f(3)=c$, $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$
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- [IIT 2001]
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- [IIT 1998]
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