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.

Why is it necessary to take the square root when finding the inverse of the function?

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What constraint is placed on x to ensure the function remains valid, and why?

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