Finding domain with e functions help

So the domain is all x and y where x+y>= ln 3.In summary, to find the domain of 1/[e^(x+y)-3], we need to first solve for e^(x+y)>=3 by taking the natural logarithm of both sides. This results in x+y being greater than or equal to ln 3. Therefore, the domain is all x and y where x+y>= ln 3.
  • #1
bart11
6
0
I'm asked to find the domain of 1/[e^(x+y)-3]

Which means I'm solving for e^(x+y)>=3

But how would I go about solving this?
 
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  • #2
e^(x+y) = e^y*e^x
 
  • #3
pickslides said:
e^(x+y) = e^y*e^x

Thanks! But hmm, I'm still confused
 
  • #4
This is supposed to help you separate x & y so you can find a function in the form of y = f(x) and find the domain from there.
 
  • #5
bart11 said:
I'm asked to find the domain of 1/[e^(x+y)-3]

Which means I'm solving for e^(x+y)>=3

But how would I go about solving this?
The only possible "difficulty" with that is that you cannot divide by 0. That, in turn, means that e^{x+y} cannot be equal to 3. So, what can x+ y not be equal to?

(To solve e^x= a, take the natural logarithm of both sides.)

Pickslide's observation that e^{x+y}= e^xe^y is true but I don't believe using that is particularly useful here.
 
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  • #6

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FAQ: Finding domain with e functions help

What is a domain in terms of e functions?

The domain of a function is the set of all possible input values for that function. For e functions, the domain consists of all real numbers or complex numbers.

How do you find the domain of an e function?

To find the domain of an e function, you need to look for any restrictions on the input values. Generally, e functions have no restrictions and thus have a domain of all real numbers or complex numbers.

Can the domain of an e function be negative?

Yes, the domain of an e function can include negative numbers. However, it is important to check for any restrictions on the input values that may limit the domain to only positive numbers.

Are there any common mistakes when finding the domain of an e function?

One common mistake is forgetting to check for restrictions on the input values. Another mistake is assuming that the domain is always all real numbers or complex numbers, when in fact there may be limitations on the input values.

Why is it important to find the domain of an e function?

Finding the domain allows you to determine the range of possible outputs for the function. It also helps you identify any restrictions on the input values that may affect the behavior of the function. Additionally, knowing the domain can help you determine if the function is well-defined and can be used in certain calculations or applications.

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