Question

Rewrite the given pair of functions as one composite formg(x)=sqrt(5x^2)x(w)=2e^wg(x(ww))=?Evalute the composite function at 1.g(x(1))=?

Composite functions
ANSWERED
asked 2021-02-26

Rewrite the given pair of functions as one composite form
\(\displaystyle{g{{\left({x}\right)}}}=\sqrt{{{5}{x}^{{2}}}}\)
\(\displaystyle{x}{\left({w}\right)}={2}{e}^{{w}}\)
\(g(x(ww))=?\)
Evalute the composite function at 1.
\(g(x(1))=?\)

Answers (1)

2021-02-27
Rewrite the given pair as one composite function as follows.
\(\displaystyle{g{{\left({x}{\left({w}\right)}\right)}}}={g{{\left({2}{e}^{{w}}\right)}}}=\sqrt{{{5}\cdot{\left({2}{e}^{{2}}\right)}^{{2}}}}\)
Evaluate the above composite function at 1
\(\displaystyle{g{{\left({x}{\left({1}\right)}\right)}}}=\sqrt{{{5}{\left({2}{e}^{{1}}\right)}^{{2}}}}=\sqrt{{{5}{\left({2}{e}\right)}^{{2}}}}=\sqrt{{{5}\cdot{4}\cdot{e}^{{2}}}}={2}\sqrt{{{5}}}{e}\approx{12.16}\)
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