# the domain and range of the function F ( t ) = t 2 + 2 t + 5 .

### 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, Problem 14RE
To determine

## To calculate : the domain and range of the function F(t)=t2+2t+5 .

Expert Solution

The domain of F(t) is (,) .

The range of F(t) is [4,) .

### Explanation of Solution

Given information : The function F(t)=t2+2t+5 is given.

Formula used : The domain of a function is the set of values that can be taken as x. The range of a function is the set of values that comes as answer to the domain.

Calculation :

To calculate the domain of F(t) , find out the acceptable values of x.

The variable t can accept any real value.

Therefore the domain of F(t)= (,) .

To calculate the range of F(t) , find out the possible answers of the function.

For 1t0 , 4F(t)5 , for the rest of the values of t F(t)>5 .

Therefore the range of F(t) = [4,) .

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