Question

If (f + g)(x) = 3x2 + 2x – 1 and g(x) = 2x – 2, what is f(x)?

3x2 + 1
3x2 – 1
3x2 + 4
3x2 – 4
x2 – 2

Answer 1

Option A is correct

`f(x)=3x^2+1`

Explanation:

Use:

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

Given that:

`(f+g)(x)=3x^2+2x-1` and g(x) = 2x-2

then;

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

Substitute the given values we have;

`3x^2+2x-1 = f(x)+2x-2`

Subtract 2x-2 from both sides we get;

`3x^2+2x-1 -2x+2= f(x)`

Combine like terms;

`f(x) = 3x^2+1`

Therefore, the function f(x) is,
`3x^2+1`

Answer 2

(f + g)(x) = 3x^2 + 2x – 1
g(x) = 2x – 2
f(x) = ? ; 3x^2 + 1

Check by Substituting:
3x^2 + 1 + 2x - 2

Simplify:
3x^2 + 2x - 1