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

In summary, the conversation is about finding the inverse of a function that is expressed as exp(y-x)+5. The person trying to solve the question thinks the solution may be y-ln(x-5), but is unsure how to get it. Another person points out that only functions have inverses and asks for clarification on what the function is a function of. Eventually, it is determined that the function is of x and the person is advised to take y as a parameter and find the inverse.
  • #1
AngryHan
2
0

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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  • #2
Welcome to PF!

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:
 
  • #3
Thanks tiny-tim :) It is a function of x I believe
 
  • #4
So, what is y? A parameter?
 
  • #5
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.
 

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

What is the inverse of an exponential function?

The inverse of an exponential function is a function in which the input and output values are reversed. In other words, the inverse function "undoes" the original exponential function.

How do you find the inverse of an exponential function?

To find the inverse of an exponential function, you can use the following steps:1. Write the original function in the form f(x) = a^x.2. Switch the x and y variables, so the function is now x = a^y.3. Solve for y by taking the logarithm of both sides.4. The resulting function is the inverse of the original exponential function.

Is the inverse of an exponential function always a function?

Yes, the inverse of an exponential function is always a function as long as the original exponential function is one-to-one (each input has a unique output). If the original exponential function is not one-to-one, the inverse will not be a function.

What is the domain and range of the inverse of an exponential function?

The domain of the inverse of an exponential function is the range of the original exponential function, and the range of the inverse is the domain of the original function. In other words, the input values of the inverse function are the output values of the original function, and vice versa.

Can an exponential function and its inverse intersect?

No, an exponential function and its inverse cannot intersect because they are mirror images of each other and therefore do not share any points. However, they may approach each other as x approaches positive or negative infinity.

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