f(x) = ln (x^2 - 1)
What is the largest domain possible for the function? Which values of x makes f(x) >(or equal to) 0, and which values makes f(x) <(or equal to) 0?
Thanks!
$\displaystyle \ln x$ is not defined (on the real numbers) for $\displaystyle x\leq0$, so the domain is all the points such that $\displaystyle x^2-1>0$.
$\displaystyle \ln x$ is non-positive for $\displaystyle 0<x\leq1$, so $\displaystyle f(x)\leq0$ when $\displaystyle 0<x^2-1\leq1$.