Find the inverse:

Question

`f\left(x\right)=\sqrt[3]{x+6}`

Answer 1

To find the inverse of a function, we swap the roles of x and y and then solve for y.

So, let's swap x and y in the function f(x):

y = & #8731; (x + 6)

Now, solve for x:

y^3 = x + 6

x = y^3 - 6

Therefore, the inverse of the function f(x) = & #8731; (x+6) is:

f^(-1)(x) = x^3 - 6