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Inverse and Domain of a function: (e^7x + 6e^-7x)/(e^7x - 7e^7x)
- Thread starter schnurben
- Start date
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Deleted member 4993
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Hi!
I am having trouble to solve this math problem:
Study this function and determine the domain and if possible the inverse.
(e^7x + 6e^-7x)/(e^7x - 7e^7x)
Any help is appreciated!
What is the definition of inverse of a function?
What does your textbook/class-notes say?
What is the definition of inverse of a function?
What does your textbook/class-notes say?
The inverse is the function does undos what the original function did.
I solved a similar problem that looked like this: f(x) = (3x+12)/(x+3), Inverse looked like this: (12-3y)/(y-3), y!=3 but I don't know how to do it with 'e'.
Thanks for your reply
This is the second time I answer you but the first one isn't showing (submitted hours ago) so I apologize if you get two answers eventually.
An inverse is a function that undoes what the original function did.
Im just having trouble doing it with 'e'. I solved a similar one earlier it looked like this:
f(x) = (3x+12)/(x+3) which gave me the inverse: x = (12-3y)/(y-3), y != 3. But I dont understand how I am supposed to get " x = something" in this one.
What is the definition of inverse of a function?
What does your textbook/class-notes say?
This is the second time I answer you but the first one isn't showing (submitted hours ago) so I apologize if you get two answers eventually.
An inverse is a function that undoes what the original function did.
Im just having trouble doing it with 'e'. I solved a similar one earlier it looked like this:
f(x) = (3x+12)/(x+3) which gave me the inverse: x = (12-3y)/(y-3), y != 3. But I dont understand how I am supposed to get " x = something" in this one.
You need grouping symbols. For example, I assume you want the e7x to actually mean e^(7x) and not (e^7)x and similarly with e^(-7x).Hi!
I am having trouble to solve this math problem:
Study this function and determine the domain and if possible the inverse.
(e^7x + 6e^-7x)/(e^7x - 7e^7x)
Any help is appreciated!
Also, are you sure of the denominator because the way it is written it is just -6e^(7x)
EDIT: BTW, for easier workings in getting the inverse, I would let t=e^(7x) and write the expression as (I think)
(t + 6/t)/(t-7/t)
Last edited:
You need grouping symbols. For example, I assume you want the e7x to actually mean e^(7x) and not (e^7)x and similarly with e^(-7x).
Also, are you sure of the denominator because the way it is written it is just -6e^(7x)
EDIT: BTW, for easier workings in getting the inverse, I would let t=e^(7x) and write the expression as (I think)
(t + 6/t)/(t-7/t)
You are correct, I missed a "-". It should be: (e^(7x) + 6e^(-7x))/(e^(7x) - 7e^(-7x)). Sorry, I should have proof-read it more carefully.
I could still use your tactic described in your edit though, right? It would be t=e^(7x):
(t + 6/t)/(t - 7/t) ?
Tried your edit
Hey, I tried the tactic in your edit and it lead me to the answer: x = (1/7) * ln(√(((-6+7y)/(1-y))
Is this the correct answer? I don't have an answer sheet.
What would you say the domain is? Obviously 1-y can't be zero but is there anything else like the whole expression has to be >0 because it's ln?
You need grouping symbols. For example, I assume you want the e7x to actually mean e^(7x) and not (e^7)x and similarly with e^(-7x).
Also, are you sure of the denominator because the way it is written it is just -6e^(7x)
EDIT: BTW, for easier workings in getting the inverse, I would let t=e^(7x) and write the expression as (I think)
(t + 6/t)/(t-7/t)
Hey, I tried the tactic in your edit and it lead me to the answer: x = (1/7) * ln(√(((-6+7y)/(1-y))
Is this the correct answer? I don't have an answer sheet.
What would you say the domain is? Obviously 1-y can't be zero but is there anything else like the whole expression has to be >0 because it's ln?