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Finding an Inverse Function Informally InExercises $7-12$ , find the inverse function of $f$ informally.Verify that $f\left(f^{-1}(x)\right)=x$ and $f^{-1}(f(x))=x$$$f(x)=6 x$$

$f(x)=6 x$$f^{-1}(x)=\frac{x}{6}=\frac{1}{6} x$$f\left(f^{-1}(x)\right)=f\left(\frac{x}{6}\right)=6\left(\frac{x}{6}\right)=x$$f^{-1}(f(x))=f^{-1}(6 x)=\frac{6 x}{6}=x$

Algebra

Chapter 1

Functions and Their Graphs

Section 9

Inverse Functions

Equations and Inequalities

Functions

Linear Functions

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but we are given the function f of X equals six X. We want to find the inverse function. And formally we just need to think about this function as the function six times X and so three idea of an inverse is to undo. And to undo this function, we need to divide each input by acts instead of multiplying. So the inverse function which we use the, uh, we just know that with a negative one looking like an exponents, the inverse function would be the input divided by six and then verify that there in verses by composing them. So first F of F inverse X would be equal to, um f of X over six, which would be equal to six times X over six, which is That's because the sixes will cancel the other direction. F inverse of f of x f a vax would be the input. So that would be, um, six x over six, which would be, well, me write it this way for you. Yeah, it would be f inverse of six X, and so that would be six x over six, which the six is canceled and we get X that way

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