# To evaluate f ( x ) = x 2 + 1 at a number, substitute the number for x in the definition of f ( x )

### 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 2.1, Problem 31E
To determine

## To evaluate f(x)=x2+1 at a number, substitute the number for x in the definition of f(x)

Expert Solution

The values of the given functionare:

f(x+2)=x2+4x+5,f(x)+f(2)=x2+6.

### Explanation of Solution

Given information:consider the function f(x)=x2+1

Calculation:

Start by assume x is the variable of a function f(x) .

Evaluate the values of the function f(x)=x2+1 for the given values of the variable x

Plug the value x=x+2, in the function f(x)=x2+1 then the value of f(x+2).

f(x+2)=(x+2)2+1f(x+2)=x2+4x+4+1f(x+2)=x2+4x+5 Use the formula (a+b)2=a2+2ab+b2

Plug the value x=2, in the function f(x)=x2+1 then the value of f(2).

f(2)=22+1f(2)=5

And,

f(x)+f(2)

=(x2+1)+5         Substitute f(x)=x2+1,f(2)=5=x2+6

Thus,the given function of the values

f(x+2)=x2+4x+5,f(x)+f(2)=x2+6.

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