Question

Given that f(x) = 4x + 5 and g(x) = x2 - 2x - 2, find (f + g)(x).

A) (f + g)(x) = x2 + 2x+3
B) (f + g)(x) = x2 + 6x+ 3
C) (f + g)(x) = -x2 + 6x + 7
D) (f + g)(x) = – x2 + 2x - 7

Answer 1

A

Explanation:

We are given the two functions:

`f(x)=4x+5\text{ and } g(x)=x^2-2x-2`

And we want to find:

`(f+g)(x)`

This is equivalent to:

`=f(x)+g(x)`

Substitute:

`=(4x+5)+(x^2-2x-2)`

Rearrange:

`=(x^2)+(4x-2x)+(5-2)`

Combine like terms. Hence:

`(f+g)(x)=x^2+2x+3`

Our answer is A.