Answer: The inverse of the function y = 2^x^2 - 4 is not a function because it is not a one-to-one function.
Explanation:
The inverse of a function is a reflection of the original function over the line y = x. To find the inverse of the function y = 2^x^2 - 4, we need to switch the variables x and y and then solve for x.
y = 2^x^2 - 4
x^2 = log2(y + 4)
x = sqrt(log2(y + 4))
However, this expression is not the inverse of the original function because it is not a one-to-one function, meaning that the same output can have multiple inputs. For example, log2(10) = 3 and log2(14) = 3.5, so sqrt(log2(10)) = sqrt(3) = sqrt(log2(14)) = sqrt(3.5). This means that for y = 10, x can be either sqrt(3) or sqrt(3.5), which is not allowed in a function.
Therefore, the inverse of the function y = 2^x^2 - 4 is not a function.