Final answer:
The inverse function f^-1 of f(x) = x^2, with the domain 0 <= x <= infinity, is f^-1(x) = sqrt(x). It's important to note that the inverse is only valid when x is non-negative to ensure it's a function.
Step-by-step explanation:
The student has asked for the formula of the inverse function, denoted as f-1, if f(x) = x2 with the domain 0 ≤ x ≤ infinity. The function f(x) = x2 is a quadratic function and its inverse can be found under the given domain constraints.
To find the inverse function, we switch the roles of x and y in the original function and solve for y, which gives us y = √x, where y ≥ 0. Therefore, the inverse function f-1(x) = √x. Remember that since the original function's domain starts at zero and goes to infinity, the inverse function should also be restricted to non-negative values of x to ensure it's a function.
Moreover, the original quadratic function x2 is only one-to-one and invertible in the domain of [0, infinity) because it is only increasing and doesn't repeat any y-values in that domain, which is crucial for the existence of an inverse function.