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Mathematics

1 answer:

exis [7]3 years ago

3 0

Answers:

$f(2) = \textbf{1}\\\\f^{-1}(1) = \textbf{2}\\\\f^{-1}(f(2)) = \textbf{2}$

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Explanation:

Replace x in f(x) with 2. Then simplify

$f(x) = \frac{1}{2}x\\\\f(2) = \frac{1}{2}(2)\\\\f(2) =1\\$

Then plug x = 1 into the inverse function and simplify

$f^{-1}(x) = 2x\\\\f^{-1}(1) = 2(1)\\\\f^{-1}(1) = 2\\$

Lastly,

$f^{-1}(f(2)) = f^{-1}(1) = 2$

is the result of combining the two parts above.

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