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

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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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