The domain of the function f(x) = ^ - 1 (3 - x) (|x| ; - 2) is - Vidyadip

MCQ

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

A
$[2, 4]$
✓
$(2, 3) \cup (3, 4]$
C
$[2,\infty)$
D
$( - \infty ,\; - 3) \cup [2,\;\infty )$

✓

Answer

Correct option: B.

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

b
(b) $f(x) = \frac{{{{\sin }^{ - 1}}(3 - x)}}{{\log \left[ {|x| - 2} \right]}}$

Let $g(x) = {\sin ^{ - 1}}(3 - x)$ ==> $ - 1 \le 3 - x \le 1$

Domain of $g(x)$ is $[2, 4]$

and let $h(x) = \log \left[ {|x| - 2} \right]$ ==> $|x| - 2 > 0$

==> $|x|\, > 2$ ==> $x < - 2$ or $x > 2$

==> $( - \infty ,\, - 2) \cup (2,\,\infty )$

we know that

$(f/g)(x) = $ $\frac{{f(x)}}{{g(x)}}\forall x \in {D_1} \cap {D_2} - \left\{ {x \in R:g(x) = 0} \right\}$

$\therefore$ Domain of $f(x) = (2,\,4] - \{ 3\} $$ = (2,\,3) \cup (3,\,4]$.

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