# If f(x) = x + 4 and g(x) = 4x^2, find (f + g)(x) and (f + g)(2).

If $$f(x) = x + 4$$ and $$\displaystyle{g{{\left({x}\right)}}}={4}{x}²$$, find $$(f + g)(x)$$ and $$(f + g)(2)$$.

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

davonliefI

Recall that $$(f+g)(x)=f(x)+g(x)$$ so:
$$\displaystyle{\left({f}+{g}\right)}{\left({x}\right)}={\left({x}+{4}\right)}+{\left({4}{x}^{{2}}\right)}$$
$$\displaystyle{\left({f}+{g}\right)}{\left({x}\right)}={4}{x}^{{2}}+{x}+{4}$$
Replacing x with 2 and evaluating, we can find $$(f+g)(2)$$. $$\displaystyle{\left({f}+{g}\right)}{\left({2}\right)}={4}{\left({2}\right)}^{{2}}+{4}$$
$$(f+g)(2)=16+2+4$$
$$(f+g)(2)=22$$