Question

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

Answer 1

Domain: `x in RR`

(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(x)` is undifined at, this would be where the denominator `=0`

`=> 1 + e^(2x) = 0`

`=> e^(2x) = -1`

`=> 2x = ln(-1)`

`=> x = 1/2 ln(-1)`

We know `1/2 ln(-1) notin RR`

So hence the denominator is defined `AAx in RR`

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

We also know `e^(2x)` is also defined `AAx in RR`

So hence `f(x)` is defined for `AAx in RR`

Domain: `x in RR`

(for all real values of `x` )