Question

what it the domain of the following functions?

1. (x^2-9)/ln(x+1)

2. Sqrt(log(x+1))

Answer 1

not quite. the domain of log is \[(0,\infty)\] so for part 1 that restriction still applies. i.e.
\[x+1>0\] so
\[x>-1\]
also you cannot divide by 0 so you also have to make sure that
\[ln(x+1)\neq 0\]
\[x+1\neq 1\]
\[x\neq 0\]
therefore domain of first one is
\[(-1,\infty), x\neq 0\]

Answer 2

second one is right