Domain of a function

**gralla55** · November 12th 2009, 07:26 AM

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!

**tonio** · November 12th 2009, 08:48 AM

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

**redsoxfan325** · November 12th 2009, 08:50 AM

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 $0<x\leq1$ , so $f(x)\leq0$ when $0<x^2-1\leq1$ .

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