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

Functions

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

2021-07-05

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 $$(f+g)(2)$$; $$\displaystyle{\left({f}+{g}\right)}{\left({2}\right)}={4}{\left({2}\right)}^{{2}}+{4}$$
$$(f+g)(2)=16+2+4$$
$$(f+g)(2)=22$$