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

\(\displaystyle{g{{\left({x}{\left({1}\right)}\right)}}}=\sqrt{{{5}{\left({2}{e}^{{1}}\right)}^{{2}}}}=\sqrt{{{5}{\left({2}{e}\right)}^{{2}}}}=\sqrt{{{5}\cdot{4}\cdot{e}^{{2}}}}={2}\sqrt{{{5}}}{e}\approx{12.16}\)

\(\displaystyle{g{{\left({x}{\left({w}\right)}\right)}}}={g{{\left({2}{e}^{{w}}\right)}}}=\sqrt{{{5}\cdot{\left({2}{e}^{{2}}\right)}^{{2}}}}\)

Evaluate the above composite function at 1

\(\displaystyle{g{{\left({x}{\left({1}\right)}\right)}}}=\sqrt{{{5}{\left({2}{e}^{{1}}\right)}^{{2}}}}=\sqrt{{{5}{\left({2}{e}\right)}^{{2}}}}=\sqrt{{{5}\cdot{4}\cdot{e}^{{2}}}}={2}\sqrt{{{5}}}{e}\approx{12.16}\)