# The domain in which the given function becomes one-to-one and find the inverse of the function with the restricted domain.

### 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 77E
To determine

## To find: The domain in which the given function becomes one-to-one and find the inverse of the function with the restricted domain.

Expert Solution

The domain in which the given function is one-to-one is [2,0] and the inverse of the function is h1(x)=x2 and domain is [0,4] .

### Explanation of Solution

Given information:

h(x)=(x+2)2

Concept used: A function with domain A is called a one-to-one function if no two elements of A have the same image, i.e.

f(x1)f(x2)    Whenever x1x2

If f be a one-to-one function with domain A and range B. Then its inverse function f1 has domain B and range A and is defined by

f1(y)=x      f(x)=y

Calculation:

From the given graph of the function, it is clear that the value of h(x) don’t repeat between x=2 and x=0 . So, in the domain [2,0] the given function is one-to-one.

h(x)=(x+2)2      2x0y=(x+2)2             0y4(x+2)=±yx=y2               [ 2x0, ignore (-ve) sign]h1(y)=y2       0y4

Therefore, the inverse of the given function with restricted domain can be written as

h1(x)=x2       [0,4]

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