To determine:

a) \(\displaystyle{h}{\left({x}\right)}={f{{\left({g{{\left({x}\right)}}}\right)}}}\)

To find h'(3)

\(\displaystyle{h}{\left({x}\right)}={f{{\left({g{{\left({x}\right)}}}\right)}}}\)

Then, \(\displaystyle{h}'{\left({x}\right)}={f}'{\left({g{{\left({x}\right)}}}\right)}\cdot{g}'{\left({x}\right)}\)

Putting x=3,

\(\displaystyle{h}'{\left({3}\right)}={f}'{\left({g{{\left({3}\right)}}}\right)}\cdot{g}'{\left({3}\right)}\)

From the given table,

\(\displaystyle{g{{\left({3}\right)}}}={2}\) and \(\displaystyle{g}'{\left({3}\right)}={9}\)

So, \(\displaystyle{h}'{\left({3}\right)}={f}'{\left({2}\right)}\cdot{9}\)

From the table, \(\displaystyle{f}'{\left({2}\right)}={5}\)

\(\displaystyle{h}'{\left({3}\right)}={5}\cdot{9}\)

\(\displaystyle{h}'{\left({3}\right)}={45}\)