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

• Feb 3rd 2009, 09:51 PM
moonman
[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
• Feb 3rd 2009, 10:08 PM
earboth
Quote:

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 $\displaystyle \mathbb{R}$ the domain of your function is $\displaystyle \mathbb{R}$ too.

But if you ask for the range of the function then $\displaystyle r = (1,\infty)$
• Feb 3rd 2009, 10:12 PM
moonman
Quote:

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

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

What do you mean by R?
So there will be no alegebra involved in this problem?
• Feb 4th 2009, 01:11 AM
earboth
Quote:

Originally Posted by moonman
What do you mean by R?
So there will be no alegebra involved in this problem?

1. $\displaystyle \mathbb{R}$ 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 $\displaystyle (2-x)~\wedge~x\in \mathbb{R}$ belong to the domain of f.