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Verify that $f$ and $g$ are inverse functions using the composition property.$$f(x)=2 x+5, g(x)=\frac{x-5}{2}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Lectures

02:08

Verify that $f$ and $g$ ar…

01:12

01:14

Use function composition t…

01:11

01:18

Use the Inverse Function P…

02:05

verify functions f and g a…

00:53

Inverse Function Property …

01:22

02:00

in Inverse Function Proper…

00:58

So if we want to verify that these are in versus the first thing we want to do is check out what is f of G of X and then we want to do in the other way as well. So, uh, this is going to be 22 times g of X plus five. And so then GM vaccines that So notice the twos cancer out with each other and we're just settle up X minus five plus five and then the fives cancel. And then we are just left with X so that one checks out. Now we can do it in the opposite order. So g of afra, Becks. So this is going to be f of X minus 5/2. And then we plug that into B two X plus five minus five all over to. So the fives cancelled. Then we have two x over two, the two's cancel, and then we're just left Live x. And so that checks out as well. So these are in verses

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