Question

find the domain of the logarithmic function:
F(x)=log[(x+7)/(x-1)]
type in interval notation

Answer 1

OS crashed on me, restarting, think about it this way, the log function is defined only for numbers > 0 in the real domain, right? Also, we cannot divide by zero. Both informations give us that x must not be -7 and must not be 1. Understanding so far?

Answer 2

So, if we choose a number > 7, we get a positive number on top and a positive in the bottom, so we are left with a positive number and we are fine. Similarly, if we pick a number < -7, we get a negative on top, a negative in the bottom, and we get a positive number and we are fine again. So x > 1 or x < -7. That is:
(-infinity, -7) U (1, +infinity)
in interval notation.