how would you do this?

Suppose that f has an inverse, f(3)=1 and f'(3)=5/3. What is (f^-1)'(1)?

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- Sep 3rd 2007, 06:14 PMrunner07inverse function derivative
how would you do this?

Suppose that f has an inverse, f(3)=1 and f'(3)=5/3. What is (f^-1)'(1)? - Sep 3rd 2007, 06:32 PMThePerfectHacker
$\displaystyle f(f^{-1}(x))=x$

Take derivative of both sides,

$\displaystyle [f^{-1}(x)]'f'(f^{-1}(x))=1$

At $\displaystyle x=1$ we have,

$\displaystyle [f^{-1}(1)]'f'(f^{-1}(1))=1$

$\displaystyle [f^{-1}(1)]'f'(3)=1$

$\displaystyle [f^{-1}(1)]'\cdot \frac{5}{3}=1$.