For the function f, of, x, equals, left parenthesis, 6, x, right parenthesis, start superscript, one third, end superscriptf(x)=(6x) 31 , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Question
For the function f, of, x, equals, left parenthesis, 6, x, right parenthesis, start superscript, one third, end superscriptf(x)=(6x) 31 , find f, to the power minus 1 , left parenthesis, x, right parenthesisf −1 (x).
Solution
To find the inverse of the function f(x) = (6x)^(1/3), we follow these steps:
- Replace f(x) with y: y = (6x)^(1/3)
- Swap x and y: x = (6y)^(1/3)
- Solve for y:
First, cube both sides to get rid of the cube root: x^3 = 6y Then, divide both sides by 6 to solve for y: y = x^3 / 6
So, the inverse function f^(-1)(x) = x^3 / 6.
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