Chapter 10: Q. 42 (page 989)

In the following exercises, find the inverse of each function.
$f (x) = 8 x$

Short Answer

Expert verified

The inverse of the function $f (x) = 8 x$ is

$f^{- 1} (x) = \frac{x}{8}$

Step by step solution

Step 1. Given data

The given function is $f (x) = 8 x$

Step 2. Substitute y for f(x)

Replace $f (x)$ with $y$

$f (x) = 8 x y = 8 x$

Step 3. Exchange x & y

Replace $x$ with $y$ and $y$ with $x$

$y = 8 x x = 8 y$

Step 4. solve the equation for y

Divide both sides of the equation by $8$

$\frac{x}{8} = \frac{8 y}{8} \frac{x}{8} = y$

Step 5. Substitute f-1(x) for y

Replace $y$ with $f^{- 1} (x)$

$\frac{x}{8} = y \frac{x}{8} = f^{- 1} (x) f^{- 1} (x) = \frac{x}{8}$

Step 6. verification

Show $f^{- 1} (f (x)) = x$

$f^{- 1} (f (x)) \overset{?}{=} x f^{- 1} (8 x) \overset{?}{=} x \frac{8 x}{8} \overset{?}{=} x x = x$

Show $f (f^{- 1} (x)) = x$

$f (f^{- 1} (x)) \overset{?}{=} x f (\frac{x}{8}) \overset{?}{=} x 8 (\frac{x}{8}) \overset{?}{=} x x = x$

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In the following exercises, find the inverse of each function.
$f (x) = 8 x$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Substitute y for f(x)

Step 3. Exchange x & y

Step 4. solve the equation for y

Step 5. Substitute f-1(x) for y

Step 6. verification

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In the following exercises, find the inverse of each function.f(x)=8x

Short Answer

Step by step solution

Step 1. Given data

Step 2. Substitute y for f(x)

Step 3. Exchange x & y

Step 4. solve the equation for y

Step 5. Substitute f-1(x) for y

Step 6. verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Statistics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the inverse of each function.
$f (x) = 8 x$