Question

question 15 of 40
if $f(x) = 2x - 5$ and $g(x) = x^2 - 4x - 8$, find $(f + g)(x)$.

a. $(f + g)(x) = x^2 - 2x - 3$
b. $(f + g)(x) = x^2 + 2x - 3$
c. $(f + g)(x) = x^2 - 2x - 13$
d. $(f + g)(x) = 3x^2 - 4x - 13$

Explanation:

Step1: Recall the definition of \((f + g)(x)\)

By the definition of function addition, \((f + g)(x)=f(x)+g(x)\).

Step2: Substitute \(f(x)\) and \(g(x)\)

Given \(f(x)=2x - 5\) and \(g(x)=x^{2}-4x - 8\), we substitute these into the formula:
\[

$$\begin{align*} (f + g)(x)&=(2x - 5)+(x^{2}-4x - 8)\\ &=x^{2}+(2x-4x)+(-5 - 8)\\ &=x^{2}-2x-13 \end{align*}$$

\]

Answer:

C. \((f + g)(x)=x^{2}-2x - 13\)