Find the domain of each function. (Enter your answers using interval notation.)

Question

(a)    f(x) = 8/1+e^x

(b)    f(x) = 5/1-e^x

 

Answer 1

for (a), we are only concerned with where 1+e^x is equal to 0 because that will make the denominator zero

there is no x that will make e^x equal to -1, so the answer in interval notation is Domain=(-∞,∞)

for (b), we are only concerned with where 1-e^x is equal to 0 because that will make the denominator zero

at x=0, e^x is equal to one. so we can't use x=0

then in interval notation our answer is Domain=(-∞,0)∪(0,∞)