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Thread: How to find the domain of this fumction?

  1. #1
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    How to find the domain of this fumction?

    The function is f(x)=ln($x+\sqrt(x^2+1)$)
    Note- The square root is over the whole $x^2+1$
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  2. #2
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    Re: How to find the domain of this fumction?

    $f(x) = \ln\left(x + \sqrt{x^2+1}\right)$

    a) we know the domain of the square root function is $x \geq 0$

    b) we know the domain of the natural log is $x > 0$

    so

    $x^2 + 1 \geq 0 \Rightarrow x \in \mathbb{R}$

    $x + \sqrt{x^2 + 1} > 0$

    this is also true for $x \in \mathbb{R}$

    so the domain of $f(x)$ is $\mathbb{R}$
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