Question

for the following pair of functions, find (f+g)(x) and (f-g)(x)

Answer 1

Given

$\begin{gathered} f(x)=4x^2+7x-5 \\ g(x)=-7x^2+3x-12 \end{gathered}$

For (f+g(x

$\begin{gathered} (f+g)x=(4x^2+7x-5)+(-7x^2+3x-12) \\ (f+g)x=4x^2+7x-5-7x^2+3x-12 \\ (f+g)x=4x^2-7x^2+7x+3x-5-12 \\ (f+g)x=-3x^2+10x-17 \end{gathered}$

For (f - g)x

$\begin{gathered} (f-g)x=(4x^2+7x-5)-(-7x^2+3x-12) \\ (f-g)x=4x^2+7x-5+7x^2-3x+12 \\ (f-g)x=4x^2+7x^2+7x-3x-5+12 \\ (f-g)x=11x^2+4x+7 \end{gathered}$