Given h(x) = 2x + 4 and f(x) = 1/2x + 3, Evaluate the composite function f[h(x)]

Question
Composite functions
asked 2021-01-08
Given \(\displaystyle{h}{\left({x}\right)}={2}{x}+{4}\) and \(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{2}}{x}+{3}\),
Evaluate the composite function f[h(x)]

Answers (1)

2021-01-09
To evaluate the composite function f(h(x)), Substitute 2x+4 in the place of h(x)
\(\displaystyle{h}{\left({x}\right)}={2}{x}+{4}\)
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{{2}{x}}}+{3}\)
\(\displaystyle{f}{\left[{h}{\left({x}\right)}\right]}={f{{\left({2}{x}+{4}\right)}}}\)
Now replace all x by 2x+4 in f(x)
\(\displaystyle{h}{\left({x}\right)}={2}{x}+{4}\)
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{{2}{x}}}+{3}\)
\(\displaystyle{f}{\left[{h}{\left({x}\right)}\right]}={f{{\left({2}{x}+{4}\right)}}}\)
\(\displaystyle{F}{\left[{\left({2}{x}+{4}\right)}\right]}=\frac{{1}}{{{2}{\left({2}{x}+{4}\right)}}}+{3}=\frac{{1}}{{{4}{x}+{8}}}+{3}\)
Answer: \(\displaystyle{f}{\left[{h}{\left({x}\right)}\right]}=\frac{{1}}{{{4}{x}+{8}}}+{3}\)
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