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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 87 (page 270)

The function $f (x) = | x |$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

Short Answer

Expert verified

The function and the inverse is

$f (x) = | x |, x 鈮� 0 f^{- 1} (x) = x, x 鈮� 0$

Step by step solution

Given information

Given the function $f (x) = | x |$

Calculating the inverse

The function is $f (x) = | x |$ . Replacing $f (x)$ with $y$ , we get

$f (x) = | x | y = x x = y f^{- 1} (x) = x (x 鈮� 0)$

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Most popular questions from this chapter

Use the graph of $y = f (x)$ given in Problem $44$ to evaluate

the following:

(a) $f (2)$

(b) $f (1)$

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Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

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(c) Verify that $h = W (h)$ is the inverse of $W = W (h)$ by showing that role="math" localid="1646158219737" $h (W (h)) = h$ and $W (h (W)) = W$ .

(d) What is the height of a male who is at his ideal weight of $80$ kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" $W (h) = 45.5 + 2.3 (h - 60)$ .

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(b) Verify that $C = C (H)$ is the inverse of $H = H (C)$ by showing that $H (C (H)) = H$ and $C (H (C)) = C$ .

A function $y = f (x)$ is increasing on the interval $(0, 5) .$ What conclusions can you draw about the graph of $y = f^{- 1} (x)$ ?

The graph of an exponential function is given. Match each graph to one of the following functions.

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91影视

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

Short Answer

Step by step solution

Given information

Calculating the inverse

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Most popular questions from this chapter

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The function $f (x) = | x |$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .