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.
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.