Answer to Question #176758 in Algebra for Jenny Navarrete

Question

Given f(x)= 3x-5, g(x)= x²-9. What is (f+g)(-2)

Answer 1

You have the following functions

$f(x)=3x-5$ and $g(x)=x^{2}-9$

The sum in the compound functions is given by

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

Obtaining the compound function

$(f+g)(x)=f(x)+g(x)\\ (f+g)(x)=3x-5+x^{2}-9\\ (f+g)(x)=x^{2}+3x-5-9\\ (f+g)(x)=x^{2}+3x-14$

Evaluating numerically at x =-2

$(f+g)(-2)=x^{2}+3x-14 \\ (f+g)(-2)=(-2)^{2}+3(-2)-14\\ (f+g)(-2)=4-6-14\\ (f+g)(-2)=-16$

Answer $\displaystyle \color{red}{\boxed{(f+g)(-2)=-16}}$