For the function f, of, x, equals, 6, start root, start index, 7, end index, x, end rootf(x)=6 7 x , find f, to the power minus 1 , left bracket, x, right bracketf −1 (x).
Question
For the function f, of, x, equals, 6, start root, start index, 7, end index, x, end rootf(x)=6 7 x , find f, to the power minus 1 , left bracket, x, right bracketf −1 (x).
Solution
The question seems to be asking for the inverse of the function f(x) = 6√x^7. Here are the steps to find the inverse:
- Replace f(x) with y: y = 6√x^7
- Swap x and y: x = 6√y^7
- Solve for y:
First, square both sides to get rid of the square root: x^2 = 36y^7 Then, divide both sides by 36 to isolate y^7: y^7 = x^2/36 Finally, take the seventh root of both sides to solve for y: y = (x^2/36)^(1/7)
So, the inverse function f^-1(x) = (x^2/36)^(1/7).
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