How to find the inverse of a quadratic that is a function

The video tutorial explains how to find the inverse of a quadratic function, h(x) = 5x^2 + 12. The process involves replacing h(x) with y, swapping x and y, and using inverse operations to solve for y. The tutorial highlights the importance of applying constraints to ensure the inverse function is valid, focusing on the positive square root and setting x to be greater than or equal to 12 to avoid negative radicands.

What is the first step to find the inverse of the function h of x = 5x² + 12?

Explain the process of swapping x and y when finding the inverse function.

What inverse operation is performed after obtaining x - 12 = 5y²?

What is the final form of the inverse function h inverse of x?

Why is it necessary to put a constraint on the values of x when finding the inverse function?