# Thread: finding the inverse function of ln

1. ## finding the inverse function of ln

Find a formula for the inverse of the function.
y = ln(x + 1)

I know that the inverse of ln(x) = e^x, but i cant figure out how to solve the inverse of ln(x+1). I tried checking my work by plugging in 3 for x and seeing if my inverse function puts out the result of ln(3+1) but no luck. Any ideas?

2. Originally Posted by evankimia
Find a formula for the inverse of the function.
y = ln(x + 1)

I know that the inverse of ln(x) = e^x, but i cant figure out how to solve the inverse of ln(x+1). I tried checking my work by plugging in 3 for x and seeing if my inverse function puts out the result of ln(3+1) but no luck. Any ideas?
What about $f^{-1}(x)= e^x-1$?

3. yes that did work. I just forgot alot of algebra. The method for getting e^x-1 would just be subtracting 1 by both sides then just putting in the inverse of ln(x) (which is e^x)?

also, how would i go about finding (f - 1)(1) and f(f -1)(1) of this? i know arctan is the inverse of tan..

4. Originally Posted by evankimia
yes that did work. I just forgot alot of algebra. The method for getting e^x-1 would just be subtracting 1 by both sides then just putting in the inverse of ln(x) (which is e^x)?
That's correct.

also, how would i go about finding (f - 1)(1) and f(f -1)(1) of this? i know arctan is the inverse of tan..
I don't quite understand the question. If you want to find the inverse of

$f(x) = 1 + x^2 + tan(\frac{\pi x}{2})$then you must write it as:

$y = 1 + x^2 + tan(\frac{\pi x}{2})$ and then change the subject of the formula (i.e. solve for x), so that it reads x=...

5. how would i go about extracting the x from the tan(pie x/2)?

I found out that f-1(1) is 0, but am not sure how. if anyone has an explanation it would be great appriciated.

6. Originally Posted by evankimia
how would i go about extracting the x from the tan(pie x/2)?

I found out that f-1(1) is 0, but am not sure how. if anyone has an explanation it would be great appriciated.
The inverse cannot be found in terms of elementary functions. Read here: http://www.mathhelpforum.com/math-he...-function.html