how to find the inverse function of f(x)=κ-e^(2-x)+x supposing that κ is a real number

Guest Jul 12, 2015

#2**+8 **

Thanks a lot.I had solved the most difficult exercises and I was stuck here,because I did not realise that you could swap x and y without doing any calculations.Imagine that I even know what I have to do next in this exercise,but my only problem was finding f^-1(x).(I had already found that f was 1-1.I am inexcusable for getting stuck here,XDDDD.Thanks man

Guest Jul 12, 2015

#1**+5 **

f(x)=κ-e^(2-x)+x

Here is a graph of f(x)

https://www.desmos.com/calculator/rr5rg1wjd3

since the mapping of x to y and y to x are both 1 to 1 I can just let f(x)=y and then swap x and y over.

function

$$y=k-e^{(2-x)}+x$$

inverse function

$$\\x=k-e^{(2-y)}+y\\$$

I should make y the subject but I cannot see how to do that.

Melody
Jul 12, 2015

#2**+8 **

Best Answer

Thanks a lot.I had solved the most difficult exercises and I was stuck here,because I did not realise that you could swap x and y without doing any calculations.Imagine that I even know what I have to do next in this exercise,but my only problem was finding f^-1(x).(I had already found that f was 1-1.I am inexcusable for getting stuck here,XDDDD.Thanks man

Guest Jul 12, 2015