The domain of the function f(x) = ^ - 1 (x - 3) 9 - x^2 is - Vidyadip

MCQ

The domain of the function $f(x) = \frac{{{{\sin }^{ - 1}}(x - 3)}}{{\sqrt {9 - {x^2}} }}$ is

A
$[1, 2)$
✓
$[2, 3)$
C
$[1, 2]$
D
$[2, 3]$

✓

Answer

Correct option: B.

$[2, 3)$

b
(b) To define $f(x)$,

$9 - {x^2} > 3 \Rightarrow - 3 < x < 3.....(i)$

$ - 1 \le (x - 3) \le 1 \Rightarrow 2 \le x \le 4.....(ii)$

From $(i)$ and $(ii)$, $2 \le x < 3$ $i.e.,\,\, [2, 3).$

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