\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1}\)

Substitute “x” by \(\displaystyle“{x}+{2}”\)

1) For \(\displaystyle{f{{\left({x}+{2}\right)}}}:\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1}\)

\(\displaystyle{f{{\left({x}+{2}\right)}}}={\left({x}+{2}\right)}^{{2}}+{1}\)

\(\displaystyle{f{{\left({x}+{2}\right)}}}={x}^{{2}}+{4}{x}+{4}+{1}\)

\(\displaystyle{f{{\left({x}+{2}\right)}}}={x}^{{2}}+{4}{x}+{5}\)

2) For \(\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}:\)

\(\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={\left({x}^{{2}}+{1}\right)}+{\left({2}^{{2}}+{1}\right)}\)

\(\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={x}^{{2}}+{1}+{4}+{1}\)

\(\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={x}^{{2}}+{6}\)