Final answer:
The function f(x) = -2x^2-4 does not have an inverse function.
Step-by-step explanation:
A function f(x) is said to have an inverse function if and only if it passes the horizontal line test, which means that no horizontal line intersects the graph of the function more than once. In other words, every value in the domain of the function must have a unique corresponding value in the range.
In this case, the given function is f(x) = -2x^2-4. To determine whether it has an inverse function, we need to verify if it passes the horizontal line test.
Let's rewrite the function as y = -2x^2 - 4 and solve for x:
-2x^2 - 4 = y
To isolate x, we can rearrange the equation as follows:
-2x^2 = y + 4
x^2 = -(y + 4)/2
x = ± √(-(y + 4)/2)
As we can see, for a given y value, there are two corresponding x values, which means the function does not pass the horizontal line test and does not have an inverse function.