# How do you find the domain of f(x)=3/(1+e^(2x))?

Dec 20, 2017

Domain: $x \in \mathbb{R}$

(defined for all values of $x$ in the real set...)

#### Explanation:

To answer this problem, the first thing we can consider is if there are any values, for what the function, $f \left(x\right)$ is undifined at, this would be where the denominator $= 0$

$\implies 1 + {e}^{2 x} = 0$

$\implies {e}^{2 x} = - 1$

$\implies 2 x = \ln \left(- 1\right)$

$\implies x = \frac{1}{2} \ln \left(- 1\right)$

We know $\frac{1}{2} \ln \left(- 1\right) \notin \mathbb{R}$

So hence the denominator is defined $\forall x \in \mathbb{R}$

( defined for all $x$ values in the real set)

We also know ${e}^{2 x}$ is also defined $\forall x \in \mathbb{R}$

So hence $f \left(x\right)$ is defined for $\forall x \in \mathbb{R}$

Domain: $x \in \mathbb{R}$

(for all real values of $x$ )