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Suppose $f^{-1}$ is the inverse function of a differentiablefunction $f$ and let $G(x)=1 / f^{-1}(x)$ . If $f(3)=2$ and$f^{\prime}(3)=\frac{1}{y}$ , find $G(2)$ .

$-1$

Calculus 1 / AB

Chapter 3

INVERSE FUNCTIONS

Section 2

Inverse Functions and Logarithms

Derivatives

Differentiation

Applications of the Derivative

Missouri State University

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Okay, so let's start by finding for us to find you prime at two. So that's ever finding, um, are derivative of G. So we can use our Kocian role. That's preservative of one, which is they're all and then minus distributive of this time at X and in times one over f inverse, that's X quiet. Okay, so we know that f evaluate at areas you could too. So since our function is, um, it has an inverse function. We also know that given this we have a inverse at two. What s equal to three. Well, that's what we need to find you prime at two. What? I see four to negative F in verse. Derivative at you over f been Ruth at two. Glad. Okay. So the derivative of our inverse function, we know that Well, that is equal to Hi there. I'm seven. We have what, over half prime at F in verse at two. This is all over a crime, or it's our f in verse right to quit. So let me simplify it out further. So we get negative one over f in this at two when an f crime and converse at two Okay, so we know what? Out of interest. Too difficult to three. So we get three squared in an F crime at three. So f prime at three deaths. With you one overnight, we get negative one over and nine times one overnight, and that's this equal to negative one.

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