Answers:
[tex]f(2) = \textbf{1}\\\\f^{-1}(1) = \textbf{2}\\\\f^{-1}(f(2)) = \textbf{2}[/tex]
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Explanation:
Replace x in f(x) with 2. Then simplify
[tex]f(x) = \frac{1}{2}x\\\\f(2) = \frac{1}{2}(2)\\\\f(2) =1\\[/tex]
Then plug x = 1 into the inverse function and simplify
[tex]f^{-1}(x) = 2x\\\\f^{-1}(1) = 2(1)\\\\f^{-1}(1) = 2\\[/tex]
Lastly,
[tex]f^{-1}(f(2)) = f^{-1}(1) = 2[/tex]
is the result of combining the two parts above.
