Question

Find the inverse of the function:

y=^{3}\sqrt{x-3}

Answer 1

Start with y = ∛(x - 3). Swap x and y to find the inverse:
x = ∛(y - 3).

Cube both sides:
x^3 = y - 3 ⇒ y = x^3 + 3.

So the inverse function is f⁻¹(x) = x^3 + 3. (Both functions have domain and range all real numbers.)