Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.
$f (x) = \frac{2 x - 3}{x + 4}$

The inverse of f is $\frac{3 + 4 x}{2 - x} .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given function is $f (x) = \frac{2 x - 3}{x + 4}$

We have to find its inverse and check the answer.

Step 2. Replace f(x) with y and interchange the variables x and y

So, $y = \frac{2 x - 3}{x + 4}$

Interchange the variables

$x = \frac{2 y - 3}{y + 4}$

Step 3. Solve for y

$x = \frac{2 y - 3}{y + 4} x (y + 4) = 2 y - 3 x y + 4 x = 2 y - 3 4 x + 3 = 2 y - x y 4 x + 3 = y (2 - x) \frac{4 x + 3}{2 - x} = y$

The inverse is $f^{- 1} (x) = \frac{4 x + 3}{2 - x} .$

Step 4. Check the answer

We can check the answers by $f^{- 1} (f (x)) a n d f (f^{- 1} (x)) .$

So,

$f^{- 1} (f (x)) = f^{- 1} (\frac{2 x - 3}{x + 4}) = \frac{4 (\frac{2 x - 3}{x + 4}) + 3}{2 - (\frac{2 x - 3}{x + 4})} = \frac{11 x}{11} = x$

Thus, $f^{- 1} (f (x)) = x$

Now,

$f (f^{- 1} (x)) = f (\frac{4 x + 3}{2 - x}) = \frac{2 (\frac{4 x + 3}{2 - x}) - 3}{(\frac{4 x + 3}{2 - x}) + 4} = \frac{11 x}{11} = x$

Thus, $f (f^{- 1} (x)) = x$

Hence our result is right.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.
$f (x) = \frac{2 x - 3}{x + 4}$

Step by Step Solution

Step 1. Given Information

Step 2. Replace f(x) with y and interchange the variables x and y

Step 3. Solve for y

Step 4. Check the answer

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

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In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer. f(x)=2x-3x+4

Step by Step Solution

Step 1. Given Information

Step 2. Replace f(x) with y and interchange the variables x and y

Step 3. Solve for y

Step 4. Check the answer

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In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.
$f (x) = \frac{2 x - 3}{x + 4}$