For the function f, of, x, equals, start root, start index, 5, end index, left parenthesis, start fraction, x, divided by, 5, end fraction, right parenthesis, end rootf(x)= 5 ( 5x ) , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Question
For the function f, of, x, equals, start root, start index, 5, end index, left parenthesis, start fraction, x, divided by, 5, end fraction, right parenthesis, end rootf(x)= 5 ( 5x ) , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Solution
To find the inverse of the function f(x) = 5√(x/5), we follow these steps:
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Replace f(x) with y: y = 5√(x/5)
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Swap x and y: x = 5√(y/5)
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Solve for y:
x/5 = √(y/5)
(x/5)² = y/5
x²/25 = y/5
y = 5x²/25
y = x²/5
So, the inverse function f^(-1)(x) = x²/5.
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