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Math Help - Domain of a function

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by gralla55 View Post
    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
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  3. #3
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    Quote Originally Posted by gralla55 View Post
    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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