Step 1

Let Given function \(\displaystyle{f{{\left({x}\right)}}}={10}{x}-{8}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={5}{x}+{7}\)

\(\displaystyle{\left({a}\right)}{\left({f}+{9}\right)}{\left({x}\right)}\)

we know that, \(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)

\(\displaystyle\Rightarrow{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)

\(\displaystyle={\left({10}{x}-{8}\right)}+{\left({5}{x}+{7}\right)}\)

\(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={15}{x}-{1}\)

Step 2

\(\displaystyle{\left({b}\right)}{\left({f}-{9}\right)}{\left({x}\right)}\)

we know that, \(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)

\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)

\(\displaystyle={\left({10}{x}-{8}\right)}-{\left({5}{x}+{7}\right)}\)

\(\displaystyle={10}{x}-{8}-{5}{x}-{7}\)

\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={5}{x}-{15}\)

Let Given function \(\displaystyle{f{{\left({x}\right)}}}={10}{x}-{8}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={5}{x}+{7}\)

\(\displaystyle{\left({a}\right)}{\left({f}+{9}\right)}{\left({x}\right)}\)

we know that, \(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)

\(\displaystyle\Rightarrow{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)

\(\displaystyle={\left({10}{x}-{8}\right)}+{\left({5}{x}+{7}\right)}\)

\(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={15}{x}-{1}\)

Step 2

\(\displaystyle{\left({b}\right)}{\left({f}-{9}\right)}{\left({x}\right)}\)

we know that, \(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)

\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)

\(\displaystyle={\left({10}{x}-{8}\right)}-{\left({5}{x}+{7}\right)}\)

\(\displaystyle={10}{x}-{8}-{5}{x}-{7}\)

\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={5}{x}-{15}\)