Inverse of a function

Calculus Level 4

If $f(x) = (2x-3\pi)^{25} + \dfrac43 x + \cos x$ and $g(x)$ is the inverse of $f(x)$ , then find $\dfrac d{dx}g(x)$ at $x = 2\pi$ .

None of these choices

\frac{30\pi^{25}+4}3

\frac73

\frac37

1 solution

Otto Bretscher
Feb 18, 2016

We have $f\left(\frac{3\pi}{2}\right)=2\pi$ and $f'\left(\frac{3\pi}{2}\right)=\frac{7}{3}$ so $g'(2\pi)=\left(f'\left(\frac{3\pi}{2}\right)\right)^{-1}=\boxed{\frac{3}{7}}$

Inverse of a function

1 solution

0 pending reports