Answer:
x = ± √((y + 2)/4)
Explanation:
To find the inverse of a function, we need to solve for x in terms of y.
Steps to find the inverse of y = 4x^2 - 2:
Replace y with x and x with y:
x = 4y^2 - 2
Solve for y:
x + 2 = 4y^2
(x + 2)/4 = y^2
± √((x + 2)/4) = y
Note that we have a ± sign because the square root of a positive number can have two values, one positive and one negative.
Therefore, the inverse of y = 4x^2 - 2 is:
x = ± √((y + 2)/4)