# Thread: Domain of a function

1. ## Domain of a function

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!

2. Originally Posted by gralla55
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!

1) The function $\displaystyle \ln x$ is defined only for $\displaystyle x>0\Longrightarrow$ in your case it must be $\displaystyle x^2-1>0$. Solve this.

2) $\displaystyle \ln x >0 \Longleftrightarrow x>1$, so in your case...

Tonio

3. Originally Posted by gralla55
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 $\displaystyle 0<x^2-1\leq1$.