Question

if $f(x)=x^{2}+16$ and $g(x)=2x^{2}-4x-3$, what is $(f+g)(x)$?

Explanation:

Step1: Define sum of functions

$(f+g)(x) = f(x) + g(x)$

Step2: Substitute given functions

$(f+g)(x) = (x^2 + 16) + (2x^2 - 4x - 3)$

Step3: Combine like terms

$(f+g)(x) = x^2 + 2x^2 - 4x + 16 - 3$

Step4: Simplify the expression

$(f+g)(x) = 3x^2 - 4x + 13$

Answer:

$3x^2 - 4x + 13$