Inverse function in exercise, analytically show that the functions are inverse functions. then use the graphing utility to show this graphically.
f(x) = e^2x
g(x) = in(x)1/2

The function is the inverse of the function

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

So, for the function swap the variables: becomes

Now, solve the equation for y.

For the function swap the variables: becomes

Now, solve the equation for y.

Therefore, the function is the inverse of the function

Here is the graph of the function and inverse. We can see that the graph of the inverse is a reflection of the actual function about the line y = x. This will always be the case with the graphs of a function and its inverse.

picture below