Find the inverse of the function y = 2x² + 2.

An inverse function is the reverse of an original function with inverse mapping. They have many interesting applications in various fields like calculus and algebra.

Answer: The inverse of the function y = 2x² + 2 is f^-1(x) = √(x - 2) / √2.

Let us proceed step by step to find the solution.

Explanation: 

From the given function

y = 2x² + 2

Since we are finding the inverse, we have to interchange the variables.

Therefore, x = 2y² + 2

Now, if we simplify the given equation further, we get:

x - 2 = 2y²

(x - 2) / 2 = y²

Now, taking square root on both sides:

y = √(x - 2) / √2

Now, after replacing y with f^-1(x), we get:

f^-1(x) = √(x - 2) / √2

Therefore, The Inverse of the function y = 2x² + 2 is f^-1(x) = √(x - 2) / √2.