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Chapter 10: Q. 40 (page 1004)

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

f(x)=x+17

Short Answer

Expert verified

The inverse of the given function isf-1x=x-17.

Step by step solution

01

Step 1. Given and explanation.

We have f(x)=x+17.

We will first replace f(x)by y. We will then replace the variables by each other. Then we will solve fory and will replaceybyf-1xto get the inverse.

02

Step 2. Replacing f(x) by y and then interchange the variable.

We have f(x)=x+17.

Replacing f(x)by ygives us y=x+17.

Interchanging the variables gives us,

x=y+17.

03

Step 3. Finding inverse.

We have x=y+17.

We need to solve for y. So, subtracting 17from both sides,

x-(17)=y+17-(17)y=x-17
Replacingybyf-1x gives us the inverse asf-1x=x-17.

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