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(C) The function is $f(x) = \frac{-5}{4x^2+1} + \sqrt{x^2-4}$.For the function to be defined,the denominator $4x^2+1$ must not be zero,and the express

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$(-\infty, -2] \cup [2, \infty)$

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(C) The function is $f(x) = \frac{-5}{4x^2+1} + \sqrt{x^2-4}$.For the function to be defined,the denominator $4x^2+1$ must not be zero,and the expression inside the square root must be non-negative.Since $4x^2+1 \geq 1$ for all $x \in R$,the denominator is never zero.For the square root,we require $x^2 - 4 \geq 0$.$x^2 \geq 4$$|x| \geq 2$This implies $x \in (-\infty, -2] \cup [2, \infty)$.Thus,the domain is $(-\infty, -2] \cup [2, \infty)$.

The domain of the function defined by $f(x) = \frac{-5}{4x^2+1} + \sqrt{x^2-4}$ is

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