Answer: C.
Step-by-step explanation:
The question is simply asking you to find a new function ((f+g)(x)) which is represented by adding f(x)+g(x) and simplifying.
So first, set up the addition.
[tex](f+g)(x)=\frac{x}{2} -3+4x^{2} +x-4[/tex]
Now, combine like terms and rearrange in order of descending powers.
[tex](f+g)(x)=4x^{2} + \frac{3}{2}x-7[/tex]
This corresponds to answer C., the correct answer.
