The domain of the function f x -1- x - x -2 iA- -1 -1- -B- -2 -2- -C- -2-1- -1-2D- -2-1 -1-2

The correct option is C ( 2, 1]∪[1,2)f(x)=√(1 |x||x| 2) For square root to be defined, nbsp; 1 |x||x| 2≥ 0 ⇒|x| 1|x| 2≤ 0 ⇒ 1≤ |x| 2 ∴ x∈( 2, 1]∪[1,2) ...

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Standard XII

Mathematics

Domain

The domain of...

Question

The domain of the function $f (x) = \sqrt{\frac{1 - | x |}{| x | - 2}}$ is

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

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(- \infty, - 2) \cup (2, \infty)

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(- 2, - 1] \cup [1, 2)

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(- 2, - 1) \cup (1, 2)

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Solution

The correct option is C $(- 2, - 1] \cup [1, 2)$
$f (x) = \sqrt{\frac{1 - | x |}{| x | - 2}}$
For square root to be defined,
$\frac{1 - | x |}{| x | - 2} \geq 0 \Rightarrow \frac{| x | - 1}{| x | - 2} \leq 0 \Rightarrow 1 \leq | x | < 2 ∴ x \in (- 2, - 1] \cup [1, 2)$

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The domain of the function f(x)=√1−|x||x|−2 is

The correct option is C (−2,−1]∪[1,2)f(x)=√1−|x||x|−2 For square root to be defined, 1−|x||x|−2≥0⇒|x|−1|x|−2≤0⇒1≤|x|<2∴x∈(−2,−1]∪[1,2)

The domain of the function $f (x) = \sqrt{\frac{1 - | x |}{| x | - 2}}$ is

The correct option is C $(- 2, - 1] \cup [1, 2)$
$f (x) = \sqrt{\frac{1 - | x |}{| x | - 2}}$
For square root to be defined,
$\frac{1 - | x |}{| x | - 2} \geq 0 \Rightarrow \frac{| x | - 1}{| x | - 2} \leq 0 \Rightarrow 1 \leq | x | < 2 ∴ x \in (- 2, - 1] \cup [1, 2)$