# Thread: [SOLVED] Find the Domain: f(x) = 2e^(2 - x) + 1

1. ## [SOLVED] Find the Domain: f(x) = 2e^(2 - x) + 1

Find the domain of this function:

f(x) = 2e^(2 - x) + 1

I'm having a very difficult time with this problem.
I do know that e is always positive and therefore the domain must be all real numbers right?
I just can't work it out algebraically.

f(x) = 2e^(2 - x) + 1

2. Originally Posted by moonman
Find the domain of this function:

f(x) = 2e^(2 - x) + 1

I'm having a very difficult time with this problem.
I do know that e is always positive and therefore the domain must be all real numbers right?
I just can't work it out algebraically.

f(x) = 2e^(2 - x) + 1
Since f(x)=e^x has the domain $\mathbb{R}$ the domain of your function is $\mathbb{R}$ too.

But if you ask for the range of the function then $r = (1,\infty)$

3. Originally Posted by earboth
Since f(x)=e^x has the domain $\mathbb{R}$ the domain of your function is $\mathbb{R}$ too.

But if you ask for the range of the function then $r = (1,\infty)$
What do you mean by R?
So there will be no alegebra involved in this problem?

4. Originally Posted by moonman
What do you mean by R?
So there will be no alegebra involved in this problem?
1. $\mathbb{R}$ is the set of all real numbers.

2. An addition of real numbers yields a real number too. Therefore (2-x) will be a real number and therefore all possible values of $(2-x)~\wedge~x\in \mathbb{R}$ belong to the domain of f.