Question

Given f(x) = x^2 - 4x + 6 and g(x) = 2x^2 + 2x - 5, what is the equation for (f + g)(x)?

Answer 1

`\\ \rm\Rrightarrow (f+g)(x)`

`\\ \rm\Rrightarrow f(x)+g(x)`

`\\ \rm\Rrightarrow x^2-4x+6+2x^2+2x-5`

`\\ \rm\Rrightarrow 3x^2-2x+1`

Done!

Answer 2

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

Explanation:

`\begin{aligned}\textsf{Given functions}: \quad f(x) &=x^2-4x+6\\g(x) &=2x^2+2x-5\\\end{aligned}`

`\begin{aligned}(f+g)(x) & =f(x)+g(x)\\& =(x^2-4x+6)+(2x^2+2x-5)\\& =x^2-4x+6+2x^2+2x-5\\& =x^2+2x^2-4x+2x+6-5\\& =3x^2-2x+1\end{aligned}`