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Verify that $f$ and $g$ are inverse functions using the composition property.$$f(x)=3 x-7, g(x)=\frac{x+7}{3}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Oregon State University

McMaster University

Lectures

01:22

Verify that $f$ and $g$ ar…

02:03

01:20

Verify that the given func…

02:04

01:54

Use the definition of inve…

01:12

01:14

Use function composition t…

03:16

Find $f(g(x))$ and $g(f(x)…

01:31

01:57

So if we want to make sure that these are compositional in versus, um, what we can do has come over here and first, um, composed with G f X and see if we get X and then do it in the other way as well. So this is going to be three times g of X minus seven g of x X plus 7/3. So these threes cancel out that we have X Plus seven minus seven, the seventh council, and then we're just left with X. So this way checks out. Now we can do it in the opposite order where we do g of f FX. So this is going to be f of X plus 7/3. So we have three x minus seven plus seven over three, the seventh council, and then we have three X over three and the Threes Council, and that will just save us with X so that one also checks out. So since when we compose them in either order, we're just left with X. That tells us we do have in verses, for they are inverse is

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