Question

If f(x) = 3 + 5x and g(x) = 2x2 – 4, find (f + g)(x).

Answer 1

Given the functions:

$\begin{gathered} f(x)=3+5x \\ g(x)=2x^2-4 \end{gathered}$

You need to add them, in order to find:

$(f+g)(x)$

Then, you have to set up:

$(f+g)(x)=(3+5x)+(2x^2-4)$

It is important to remember the Sign Rules for Multiplication:

$\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}$

Then:

$(f+g)(x)=3+5x+2x^2-4$

By adding the like terms (these are defined as those terms that have the same variables with the same exponents), you get:

$(f+g)(x)=2x^2+5x-1$

Hence, the answer is: First option.