# The inverse of the function g ( x ) = f ( x + c ) .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.6, Problem 62E

(a)

To determine

## To find:The inverse of the function g(x)=f(x+c) .

Expert Solution

### Explanation of Solution

Given:

The function is g(x)=f(x+c) .

The graph of inverse function is the image of the function with respect to y=x .

If a graph is shifted x units to left it corresponds to the shift down to the graph of the inverse function.

Thus, if

g(x)=f(x+c)

Then,

g1(x)=f1(x)c

Therefore, the inverse is g1(x)=f1(x)c .

(b)

To determine

Expert Solution

### Explanation of Solution

Given:

The function is h(x)=f(cx) .

If h(x) is the curve of f(x) compressed horizontally by a factor c then h1(x) is the curve of f1(x) compressed vertically by a factor of c .

h1(x)=1cf1(x)

Therefore, the inverse is h1(x)=1cf1(x) .

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