Final answer:
The inverse of the function f(x) = 8 square root of x is f^(-1)(x) = x^2/64 for x ≥ 0.
Step-by-step explanation:
To find the inverse of the function f(x) = 8 square root of x, we need to switch the roles of x and y.
Start by replacing f(x) with y: y = 8 square root of x.
Next, swap x and y: x = 8 square root of y.
Solve for y: square both sides of the equation to get x^2 = 64y, then divide both sides by 64 to get y = x^2/64.
Therefore, the inverse of f(x) = 8 square root of x is f^(-1)(x) = x^2/64 for x ≥ 0.