Question

Find the inverse of the following function: f(x) = 5x², for x ≥ 0.

Answer 1

The inverse of the function f(x) = 5x² for x ≥ 0 is f^(-1)(x) = √(x/5).

Step-by-step explanation:

To find the inverse of the function f(x) = 5x² for x ≥ 0, we need to swap the x and y variables and solve for y.

Step 1: Replace f(x) with y: y = 5x²

Step 2: Swap x and y: x = 5y²

Step 3: Solve for y: y² = x/5

Step 4: Take the square root of both sides: y = ±√(x/5)

Since x should be non-negative according to the original function's domain, we take the positive square root, so the inverse function is given by f^(-1)(x) = √(x/5)