Inverse function of bi-exponential function?

[f_coco]

Homework Statement

What is the inverse function of a bi-exponential function like the following:
Y=A*exp(B*X)+C*exp(D*X)

Homework Equations

Y=A*exp(B*X)

The Attempt at a Solution

If it is a single exponential function, i can take log on both sides to get inverse function. But when it comes to a bi-exponential function, i really don't know how to do it. Thanks in advance.

 

[Dick]

If y(x)=(1/2)(e^x+e^(-x)) (that's the cosh function), then y(1)=y(-1). It doesn't even have an inverse.

 

[f_coco]

In fact, the bi-exponential equation i described here is a bi-exponential decay equation. The domain of X is 0 to inf. The parameter A and C should be greater than 0 and B, D should be less than 0. I have plotted a simulated data with R. It seems the inverse function of the bi-exponential function should be a multiple logarithmic function.

 

[Dick]

Ok, if you restrict the domain, then it can have an inverse. But I don't think there is a nice way to solve for x in terms of y except in special cases. You'll have to use graphical or numerical techiques to get an approximate solution. As you've noticed, logs don't get you there.