# Evaluate the indicated expressions and simplify. f(x) = x^2 + 1, f(x + 2) , f(x) + f(2).

Question
Analyzing functions
Evaluate the indicated expressions and simplify.
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1},{f{{\left({x}+{2}\right)}}},{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}.$$

2021-02-10
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1}$$
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 $$\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}:$$
$$\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={\left({x}^{{2}}+{1}\right)}+{\left({2}^{{2}}+{1}\right)}$$
$$\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={x}^{{2}}+{1}+{4}+{1}$$
$$\displaystyle{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}={x}^{{2}}+{6}$$

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