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Verify that $f$ and $g$ are inverse functions using the composition property.$$f(x)=5 x+9, g(x)=\frac{x-9}{5}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Lectures

01:02

Verify that $f$ and $g$ ar…

01:14

Use function composition t…

02:30

02:08

00:45

02:07

Find $f(g(x))$ and $g(f(x)…

03:30

01:55

So if we want to confirm that these are inverse is, um the first thing we can do is go ahead and look at F composed with G F X and then see if this just output tax So this is going to be five times G of X plus nine. So we go ahead and plug that into the five times X minus 9/5 plus five. So the fives cancel and then we have X minus nine plus nine, the nines we're going to cancel, and then we just have where this is X so that one checks out. Now we need to do it in the opposite order as well. So g of f of X is going to be so f of X minus 9/5 and then after a nexus five X plus nine that we have minus 95. So these nines cancel. That gives us five X over five. The fives cancel, and then we'll just have to live X. So you can see that we compose these in either order and we are just left with X

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