Domain of the real valued function f(x) = log | vedclass

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(C) For the function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ to be defined:$1$. The argument of the logarithm must be positive: $x^2 - 1

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$R - [-1, 1]$

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(C) For the function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ to be defined:$1$. The argument of the logarithm must be positive: $x^2 - 1 > 0$,which implies $x^2 > 1$,so $x \in (-\infty, -1) \cup (1, \infty)$.$2$. The inverse hyperbolic cotangent function $\operatorname{coth}^{-1} x$ is defined for $|x| > 1$,which means $x \in (-\infty, -1) \cup (1, \infty)$.Combining both conditions,the domain is $x \in (-\infty, -1) \cup (1, \infty)$,which can be written as $R - [-1, 1]$.

Domain of the real valued function $f(x) = \log(x^2 - 1) + x \operatorname{coth}^{-1} x$ is

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