Find the function definition for the first composite function, as follows:

\(\displaystyle{\left({q}\circ{r}\right)}{\left({x}\right)}={q}{\left({r}{\left({x}\right)}\right)}\)

\(\displaystyle={q}{\left(\sqrt{{{x}+{8}}}\right)}\)

\(\displaystyle={\left(\sqrt{{{x}+{8}}}^{{2}}+{7}\right.}\)

\(\displaystyle={x}+{8}+{7}\)

\(\displaystyle={x}+{15}\)

Find the function definition for the second composite function, as follows:

\(\displaystyle{\left({r}\circ{q}\right)}{\left({x}\right)}={r}{\left({q}{\left({x}\right)}\right)}\)

\(\displaystyle={r}{\left({x}^{{2}}+{7}\right)}\)

\(\displaystyle=\sqrt{{{\left({x}^{{2}}+{7}\right)}+{8}}}\)

\(\displaystyle=\sqrt{{{x}+{15}}}\)

Find the value of the first composite function at x=1, as follows:

\(\displaystyle{\left({q}\circ{r}\right)}{\left({1}\right)}={\left({1}\right)}+{15}={16}\)

Find the value of the second composite function at x=1, as follows:

\(\displaystyle{\left({r}\circ{q}\right)}{\left({1}\right)}=\sqrt{{{1}^{{2}}+{15}}}\)

\(\displaystyle=\sqrt{{16}}\)

=4

\(\displaystyle{\left({q}\circ{r}\right)}{\left({x}\right)}={q}{\left({r}{\left({x}\right)}\right)}\)

\(\displaystyle={q}{\left(\sqrt{{{x}+{8}}}\right)}\)

\(\displaystyle={\left(\sqrt{{{x}+{8}}}^{{2}}+{7}\right.}\)

\(\displaystyle={x}+{8}+{7}\)

\(\displaystyle={x}+{15}\)

Find the function definition for the second composite function, as follows:

\(\displaystyle{\left({r}\circ{q}\right)}{\left({x}\right)}={r}{\left({q}{\left({x}\right)}\right)}\)

\(\displaystyle={r}{\left({x}^{{2}}+{7}\right)}\)

\(\displaystyle=\sqrt{{{\left({x}^{{2}}+{7}\right)}+{8}}}\)

\(\displaystyle=\sqrt{{{x}+{15}}}\)

Find the value of the first composite function at x=1, as follows:

\(\displaystyle{\left({q}\circ{r}\right)}{\left({1}\right)}={\left({1}\right)}+{15}={16}\)

Find the value of the second composite function at x=1, as follows:

\(\displaystyle{\left({r}\circ{q}\right)}{\left({1}\right)}=\sqrt{{{1}^{{2}}+{15}}}\)

\(\displaystyle=\sqrt{{16}}\)

=4