Question

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

–4
–2
2
4

Answer 1

f(x) = x^2 - 2x
g(x) = 6x + 4

(f + g)(x)......so we add them
x^2 - 2x + 6x + 4 = 0
x^2 + 4x + 4 = 0
(x + 2)(x + 2) = 0
(x + 2)^2 = 0

x + 2 = 0
x = -2 <====

Answer 2

Answer: -2

Explanation:

The given functions :
`f(x) = x^2-2x\text{ and }g(x) = 6x + 4`

Then the combine function of the above function is given by :-

`(f + g)(x)=\f(x)+g(x)=x^2-2x+6x+4=x^2+4x+4`

Factorize
`(f + g)(x)=x^2+4x+4` by splitting middle term.

`=x^2+2x+2x+4\\\\=x(x+2)+2(x+2)\\\\=(x+2)(x+2)`

Substitute
`(f + g)(x) = 0`

`(x+2)(x+2)=0\\\\\Rightarrow\ x=-2`

Hence, at x=-2
`(f + g)(x) = 0`