Question

The domain of the function f(x)=5/(1+e^x) (in interval notation)

Answer 1

what is the main concern here? when looking at fractions, what gives us troubles?

Answer 2

Well I know 2<e<3 and I also know that x is not equal to zero but I do not know how to express the answer in interval form.

Answer 3

.... the domain of a function are all the values that we are allowed to use that will not make our function go bad. fractions go bad when we divide by zero right?

when does 1+e^x = 0?

Answer 4

That's where I get stuck. I just don't know how to work out the problem to get the answer.

Answer 5

the answer lies in knowing something about e^x; this always produces a positive value.

1 + some positive value is never 0; so our domain, the stuff we are allowed to use for "x" is not restricted in any way:

D = (-inf,inf)

Answer 6

Thank you! It was the "e" throwing me off the whole time. I felt like I needed to divide it or do natural log for some reason.

Answer 7

you could have tried to log it but the effects the same without knowing the properties of exponential and logarithmic functions.

1+ e^x = 0

e^x = -1

ln(e^x = -1)

x = ln(-1) ; since the value of ln(-1) is not defined for the real number set; its just something that has to be "known"