# Whether the statement that inverse function f − 1 ( x ) is always the same as 1 f ( x ) , is true or false.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.7, Problem 4E

(a)

To determine

## Whether the statement that inverse function f−1(x) is always the same as 1f(x) , is true or false.

Expert Solution

The statement that inverse function f1(x) is always the same as 1f(x) , is false.

### Explanation of Solution

Function 1f(x) resembles as [f(x)]1 .

That does not equal to the inverse function f1(x) , both are different and gives different outputs.

Thus, the statement that inverse function f1(x) is always the same as 1f(x) , is false.

(b)

To determine

### Whether the statement that inverse function f−1(f(x)) is equal to the x , is true or false.

Expert Solution

The statement that inverse function f1(f(x)) is equal to the x , is true.

### Explanation of Solution

Function f in terms of x f(x) has an inverse.

Let function f(x) is equal to y.

f(x)=y (1)

Then, the inverse function is to be,

f1(y)=x .

Substitute f(x) for y from equation (1) in above equation,

f1(f(x))=x .

Thus, the statement that inverse function f1(f(x)) is equal to the x , is true.

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