y = 100e^(-2x) Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

We are asked to determine if the function y=100e^(-2x) has an inverse function by finding if the function is strictly monotonic on its entire domain using the derivative. The domain is all real numbers.
y'=-200e^(-2x) and y'<0 for all real x so the function is strictly monotonic (in this case strictly decreasing) and therefore has an inverse function.
The graph: