Question

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

Functions
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asked 2021-07-04

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

Answers (1)

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

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