Inverse of the natural logarithms

[Wingman]

Hi Guys, i am new to this forums and my english is poor, but i will do my best.

I got stuck with this problem, i think it's quite easy, but i get the wrong answer

F(x) = ln(1+e^x)

1. Show that it has an inverse
2. What is the Range And the Domain of the inverse.

I really appreciate a good solution so i can learn from my mistakes.

 

[arildno]

1. Show that F is a strictly increasing function.
2. The domain of the inverse is the range of F and vice versa.
3. Welcome to PF!

 

[Wingman]

so the inverse must be ln(e^x-1)?

 

[arildno]

Yeah, that seems right.

 

[Wingman]

The domain must be then; ]0, infinity[ And the range]-1, Infinity[ or am i wrong?

 

[arildno]

Your domain is correct, but the range of the inverse is from negative to positive infinity.

 

[Wingman]

of course, how stuiped of me Thx for the help!