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

1 Answer
Dec 20, 2017

Answer:

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# )

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