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In $3-10,$ find each of the function values when $\mathrm{f}(x)=4 x$$$\mathrm{f}\left(\mathrm{f}^{-1}(-6)\right)$$

$-6$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 8

Inverse Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

McMaster University

Baylor University

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Hi, everybody. The deception 4.8. Number eight on it. It says that f of X is equal to four X and we have to find f of F in verse of negative six. So there are a few ways to go about this problem. One way to do it is let's first find the inverse. How do you find the inverse of the function? Well, this function is why equals four X. And to find the inverse, we have to switch the X and Y so X is equal to four. Why, Uh, okay, and now we want to solve for the new Why. So we divide both sides by four, and we get why is equal to X over four. So that is our inverse function. F in verse is X over four. So if we plug in a negative six f inverse of negative six would be negative. Six over four or it reduces to negative three halves. Now we want to find f of negative 3/2 how we find f of negative three halves. We plug it into the X right here. So it's four x. What is X negative? Three over two on When we evaluate this, we get four times negative. Three over two is negative. 12 over, too is negative. Six. And that's our answer. Well, what do you notice? Look at the question and look at the answer. Well, ah, function and its inverse right. What's gonna happen when you compose them? You get X, you get what you plugged in. So because this was the question, this is going to be the answer. There's no issue with restrictions. This is a linear function. The answer is negative. Six. So you could have done it the short way or the longer way.

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