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

Question
Analyzing functions
asked 2021-02-09
Evaluate the indicated expressions and simplify.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{1},{f{{\left({x}+{2}\right)}}},{f{{\left({x}\right)}}}+{f{{\left({2}\right)}}}.\)

Answers (1)

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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