Question

I just need step by step explanation please that would help me out very much.

Answer 1

Given

$\begin{gathered} f(x)=2x+1 \\ g(x)=x^2-7 \end{gathered}$

To find

$(f+g)(x)$

Step 1

$Add\text{ f(x) to }g(x)\text{ to obtain (f+g)(x)}$$\begin{gathered} f(x)\text{ + g(x)=(f+g)(x)} \\ (f+g)(x)=(2x+1)+(x^2-7) \\ (f+g)(x)=x^2+2x-7+1 \\ (f+g)(x)=x^2+2x-6 \end{gathered}$

Hence, the answer is option D