# Domain of a function

• Nov 12th 2009, 08:26 AM
gralla55
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!
• Nov 12th 2009, 09:48 AM
tonio
Quote:

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

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

Tonio
• Nov 12th 2009, 09:50 AM
redsoxfan325
Quote:

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!

$\ln x$ is not defined (on the real numbers) for $x\leq0$, so the domain is all the points such that $x^2-1>0$.

$\ln x$ is non-positive for $0, so $f(x)\leq0$ when $0.