EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3, Problem 13CLT

To determine

if the inverse of function h(x)=3x−4 exists and if so, then find the inverse.

Expert Solution & Answer

Answer to Problem 13CLT

h−1(x)=13(x+4)

Explanation of Solution

Concept Used:

Horizontal Line Test:

The inverse function for a function f exists if and only if no horizontal line intersects its graph at more than one point .

The graph of the function h(x)=3x−4 is given below:

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 13CLT

Clearly, no horizontal line intersects the graph of f at more than one point, so f is a one-to-one function and does have an inverse function.

Let y=h(x) , then the given function can be written as:

y=3x−4

Now, to find the inverse function, interchange the variables x and y and then solve of y .

x=3y−43y=x+4y=13(x+4)

So, the inverse of the function h(x)=3x−4 is h−1(x)=13(x+4) .

Chapter 3, Problem 12CLT

Chapter 3, Problem 14CLT

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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if the inverse of function h ( x ) = 3 x − 4 exists and if so, then find the inverse.

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if the inverse of function h(x)=3x−4 exists and if so, then find the inverse.

Answer to Problem 13CLT

Explanation of Solution

Chapter 3 Solutions