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.