Question

question 5 of 10
for $f(x) = 2x + 1$ and $g(x) = x^2 - 7$, find $(f + g)(x)$.

a. $2x^3 - 6$

b. $2x^2 - 15$

c. $x^2 + 2x - 6$

d. $x^2 + 2x + 8$

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \((f + g)(x)\) is defined as \(f(x) + g(x)\).

Step2: Substitute the given functions

We know \(f(x)=2x + 1\) and \(g(x)=x^{2}-7\). So, \((f + g)(x)=f(x)+g(x)=(2x + 1)+(x^{2}-7)\).

Step3: Combine like terms

Remove the parentheses: \(2x + 1+x^{2}-7\). Then combine the constant terms: \(1-7=-6\). So the expression becomes \(x^{2}+2x - 6\).

Answer:

C. \(x^{2}+2x - 6\)