First slide

Functions (XII)

Question

The domain of f(x)= $\frac{\sin^{- 1} (3 - x)}{\log (|x| - 2)}$ is

Moderate

A

[2,4]
B

(2,3) $\cup$ (3,4]
C

[2, $\infty$ )
D

none of these

Solution

Given,f(x)= $\frac{\sin^{- 1} (3 - x)}{\log (|x| - 2)}$
let g(x)= $\sin^{- 1} (3 - x) \Rightarrow - 1 \leq 3 - x \leq 1$
The domain of g(x) is [2,4]
Let h(x)=log $(|x| - 2)$ $\Rightarrow |x| - 2 > 0 o r |x| > 2 a n d x \neq \pm 3$
$\Rightarrow x < - 2 o r x > 2$
$∴$ Domain $(- \infty, - 2) \cup (2, \infty)$
We know that
$(\frac{f}{g})$ (x)= $\frac{f (x)}{g (x)}$ ,x $\in$ D₁ $\cap$ D₂ $- {x \in R, g (x) = 0}$
Hence the domain of f(x)is (2,4]-{3}
i.e (2,3) $\cup$ (3,4]

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