find the inverse

Question

f(x)=^3√x+6
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Answer 1

To find the inverse of f(x) = cubed_root(x) + 6, we can follow these steps:

1. Let y = cubed_root(x) + 6
2. Swap x and y: x = cubed_root(y) + 6
3. Solve for y in terms of x:

x = cubed_root(y) + 6
x - 6 = cubed_root(y)
(x - 6)^3 = y
y = (x - 6)^3

4. Therefore, the inverse of f(x) = cubed_root(x) + 6 is f^(-1)(x) = (x - 6)^3.