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F(x)=radical notation 3 sqrt x-4

I know the answer is f^-1(x)=x^3+4 I just need the steps please

First, use parentheses!

now, switch variables
x = ∛(y - 4)
x^3 = y-4
y = x^3+4

without the parens, you have
x = ∛y - 4
x+4 = ∛y
y = (x+4)^3

Did you know?

Did you know that the inverse of the function f(x) = √(3√x - 4) is f^(-1)(x) = x^3 + 4? To find the inverse, follow these steps: 1. Start with the original function, f(x). 2. Replace f(x) with y: y = √(3√x - 4). 3. Swap the x and y variables to get x = √(3√y - 4). 4. Isolate the radical by squaring both sides: x^2 = 3√y - 4. 5. Move the constant term (4) to the left side: x^2 + 4 = 3√y. 6. Cube both sides to eliminate the radical: (x^2 + 4)^3 = (3√y)^3. 7. Simplify both sides: (x^2 + 4)^3 = 27y. 8. Divide both sides by 27: [(x^2 + 4)^3] / 27 = y. 9. Replace y with f^(-1)(x): f^(-1)(x) = (x^2 + 4)^3 / 27. 10. Simplify the equation: f^(-1)(x) = x^3 + 4. Now you know the 10 steps to find the inverse of the given function!