inverse function of y=-2e^x

Help please, Thanks!

To find the inverse function of y = -2e^x, we need to swap the positions of x and y and solve for the new y.

Let's start by swapping x and y:

x = -2e^y

Now, let's isolate y. Divide both sides of the equation by -2:

x/-2 = e^y

Next, we need to take the natural logarithm (ln) of both sides to undo the exponential function:

ln(x/-2) = y

Therefore, the inverse function is:

f^-1(x) = ln(x/-2)

So, the inverse function of y = -2e^x is f^-1(x) = ln(x/-2).

Remember that the inverse function undoes the effect of the original function.