First slide

Functions (XII)

Question

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

Moderate

A

(–∞, ∞)\[–1, 1]
B

(–∞, ∞)\[–2, 2]
C

[–1, 1] ∪ (–∞, –2) ∪ (2, ∞)
D

None of these

Solution

f (x) is defined if $\frac{1 - | x |}{2 - | x |} \geq 0 and 2 - | x | \neq 0$
$\begin{array}{l} \Rightarrow \frac{(1 - | x |) (2 - | x |)}{(2 - | x |)^{2}} \geq 0 and x \neq - 2, 2 \\ \Rightarrow (| x | - 1) (| x | - 2) \geq 0 and x \neq - 2, 2 \\ \Rightarrow | x | \leq 1 or | x | > 2 \\ \Rightarrow - 1 \leq x \leq 1 or (x < - 2 or x > 2) \\ Domain of f = [- 1, 1] \cup (- \infty, - 2) \cup (2, \infty) \end{array}$

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