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Chapter 10: Q. 10.15 (page 1000)

Find the inverse of the function

f(x)=5x-3

Short Answer

Expert verified

The inverse of f(x)=5x-3is

f-1(x)=x+35

Step by step solution

01

Given information

Given the functionf(x)=5x-3

02

Replace f(x) with y and then x,y

Replacing, we get

f(x)=5x-3y=5x-3x=5y-3x+3=5yy=x+35

03

Substitute f-1(x) for y

Substituting, we get

f-1(x)=x+35

04

Verify f(f-1(x))=x

Substituting the values, we get

f(x+35)=5(x+35)-3f(x+35)=x+3-3f(x+35)=x

So the functions are inverses

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Most popular questions from this chapter

In the following exercises, solve each equation.

e2x路e3=e9

Convert from exponential to logarithmic form:

32x=324.

In the following exercises, find the inverse of each function.

f(x)=6x-7

In the following exercises, graph each function in the same coordinate system:

f(x)=2x,g(x)=2x-1

Convert from exponential to logarithmic form:

3-2=19.
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