find the domain of 8/8 + e^x using interval notation

Question

 I need help finding the domain and putting it in interval notation.

Answer 1

Hmm, the expression you wrote is equivalent to (8/8) + e^x = 1 + e^x.  I think you meant:

 

     8/(8+e^x)

 

e^x is defined for all values of x.  The only restriction on the domain, then, would be when e^x = -8 since that would make the denominator equal zero and division by 0 is undefined.

 

     e^x = -8

     x = ln(-8)

 

You can't take the log of a negative number, so there is no value of x such that e^x = -8.  Hence the expression 8/(8+e^x) is defined for all x.  In interval notation: (-∞,∞)