Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find the inverse of the linear function $f (x) = m x + b m \neq 0$

The inverse of the function $f (x) = m x + b m \neq 0$ is $f^{- 1} (x) = \frac{x - b}{m} m \neq 0$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given data

The given function is

$f (x) = m x + b m \neq 0$

Step 2. interchanging variables

Replace $f (x)$ with y and interchange x and y

role="math" localid="1646177714686" $f (x) = m x + b y = m x + b x = m y + b$

Step 3. The inverse of the function

Solve the equation for y

$x = m y + b x - b = m y \frac{x - b}{m} = y y = \frac{x - b}{m}$

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

role="math" localid="1646177950266" $f^{- 1} (x) = \frac{x - b}{m} m \neq 0$

Step 4. Verification

Determine $f (f^{- 1} (x))$

$f (f^{- 1} (x)) = f (\frac{x - b}{m}) f (f^{- 1} (x)) = m (\frac{x - b}{m}) + b f (f^{- 1} (x)) = x - b + b f (f^{- 1} (x)) = x$

Determine $f^{- 1} (f (x))$

$f^{- 1} (f (x)) = f^{- 1} (m x + b) f^{- 1} (f (x)) = \frac{(m x + b) - b}{m} f^{- 1} (f (x)) = \frac{m x}{m} f^{- 1} (f (x)) = x$

$f^{- 1} (f (x)) = x & f (f^{- 1} (x)) = x$ so inverse function is correct

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find the inverse of the linear function $f (x) = m x + b m \neq 0$

Step by Step Solution

Step 1. Given data

Step 2. interchanging variables

Step 3. The inverse of the function

Step 4. Verification

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find the inverse of the linear functionf(x)=mx+bm≠0

Step by Step Solution

Step 1. Given data

Step 2. interchanging variables

Step 3. The inverse of the function

Step 4. Verification

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Find the inverse of the linear function $f (x) = m x + b m \neq 0$