What is the inverse function of f(x) = -A*ln(1-x) +B*x ?

Question

A and B are constants. Is this possible to solve? I'm stuck. Help is much appreciated.

Answer 1

You can start by letting y = f(x) and then solving for x in terms of y, which you probably already did. But unfortunately, no, I don't think there's an analytical way to find the inverse from there. Having the x inside and outside of the natural log like that makes it (as far as I can tell) impossible.

Answer 2

First, the question is severaly incorrect. A graph would not have an inverse. A function has an inverse. So the 1st ingredient would desire to be figuring out the function in question. It feels like the student has the common extreme college confusion of equation and overall performance. i think of you should convey interior the right set theoretic view to make clean this. So tell him that the "genuine" thank you to view a function is as 2 gadgets, and a rule that maps between them. y=x^2 is in basic terms an equation, what's considerable is that it is mapping from R to R. If he desires to define an inverse, that's large, yet tell him you pick 3 issues: the area, the variety, and the rule of thumb. with out those 3 issues, in spite of you're conversing approximately isn't a function.

Answer 3

To get the inverse all you have to do is switch the x and y values. f(x) = y
The inverse function would be:

x=-A*In(1-y)+B*y

If it dosent say to solve .. then it dosent matter that A and B are constants .. that answer IS the inverse function.

Answer 4

y=-Aln(1-x) +Bx
To find x=g(y) is nor possible algebraically .For each given y
you can solve the equation numerically.

Answer 5

Better not tell you now.

Answer 6

its ok to say 'I dont know.' eight ball.