How do you find the inverse of an exponential function with multiple variables?

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To find the inverse of the function exp(y-x) + 5, it is essential to clarify that this expression involves both x and y. The discussion suggests treating y as a parameter while defining the function in terms of x, leading to f(x) = t = exp(y-x) + 5. To solve for the inverse, one must isolate x in terms of t and y. The confusion arises from the relationship between x and y, highlighting the need for a clear definition of the function's variables. Understanding these relationships is crucial for accurately determining the inverse.
AngryHan
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Homework Statement



Find the inverse of exp(y-x)+5

2. The attempt at a solution

I think the solution is y-ln(x-5) but I can't think of how to solve it to get that. I don't know what to do about the x and the y being together.
 
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Hi AngryHan! Welcome to PF! :smile:
AngryHan said:
Find the inverse of exp(y-x)+5

This question makes no sense. :frown:

Only functions have inverses.

What is this a function of? x? y? y-x? :confused:​
 
Thanks tiny-tim :) It is a function of x I believe
 
So, what is y? A parameter?
 
I believe you need to take y to be a parameter, and let the function be

f(x) = t = exp(y-x)+5

Now, try to find the inverse.
 

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