The domain of the function fx=2x−1x2−10x−113 is

fx=2x−1x2−10x−113 is defined iffx2−10x−11≠0⇒ x2−11x+x−11≠0⇒xx−11+1x−11≠0⇒x+1x−11≠0⇒ x≠−1, 11∴ x∈−∞, −1∪−1, 11∪11,∞

The domain of the function fx=2x−1x2−10x−113 is

fx=2x−1x2−10x−113 is defined iffx2−10x−11≠0⇒ x2−11x+x−11≠0⇒xx−11+1x−11≠0⇒x+1x−11≠0⇒ x≠−1, 11∴ x∈−∞, −1∪−1, 11∪11,∞

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$T h e d o m a i n o f t h e f u n c t i o n f (x) = \sqrt[3]{\frac{2 x - 1}{x^{2} - 10 x - 11}} i s$

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$(- \infty, \infty)$

$(- \infty, 0)$

$(0, \infty)$

$(- \infty, - 1) \cup (- 1, 11) \cup (11, \infty)$

answer is C.

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Detailed Solution

$\begin{array}{l} f (x) = \sqrt[3]{\frac{2 x - 1}{x^{2} - 10 x - 11}} i s d e f i n e d i f f \\ x^{2} - 10 x - 11 \neq 0 \\ \Rightarrow x^{2} - 11 x + x - 11 \neq 0 \\ \Rightarrow x (x - 11) + 1 (x - 11) \neq 0 \\ \Rightarrow (x + 1) (x - 11) \neq 0 \\ \Rightarrow x \neq - 1, 11 \\ ∴ x \in (- \infty, - 1) \cup (- 1, 11) \cup (11, \infty) \end{array}$