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 is $f^{- 1} x = x - 17$ .

Step by step solution

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 for $y$ and will replace $y$ by $f^{- 1} x$ to get the inverse.

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

We have $f (x) = x + 17$ .

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

Interchanging the variables gives us,

$x = y + 17$ .

Step 3. Finding inverse.

We have $x = y + 17$ .

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

$x - (17) = y + 17 - (17) y = x - 17$
Replacing $y$ by $f^{- 1} x$ gives us the inverse as $f^{- 1} x = x - 17$ .

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In the following exercises, find the inverse of each function.
$f (x) = x + 17$

Short Answer

Step by step solution

Step 1. Given and explanation.

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

Step 3. Finding inverse.

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In the following exercises, find the inverse of each function.f(x)=x+17

Short Answer

Step by step solution

Step 1. Given and explanation.

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

Step 3. Finding inverse.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Geometry

Statistics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, find the inverse of each function.
$f (x) = x + 17$