Given the functions:
[tex]\begin{gathered} f(x)=3+5x \\ g(x)=2x^2-4 \end{gathered}[/tex]
You need to add them, in order to find:
[tex](f+g)(x)[/tex]
Then, you have to set up:
[tex](f+g)(x)=(3+5x)+(2x^2-4)[/tex]
It is important to remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]
Then:
[tex](f+g)(x)=3+5x+2x^2-4[/tex]
By adding the like terms (these are defined as those terms that have the same variables with the same exponents), you get:
[tex](f+g)(x)=2x^2+5x-1[/tex]
Hence, the answer is: First option.
