First slide

Functions (XII)

Question

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

Moderate

A

$[1, 2]$
B

$[2, 3)$
C

$[1, 3)$
D

$[2, 1]$

Solution

$- 1 \leq x - 3 \leq 1$ and $9 - x^{2} > 0$
$\Rightarrow 2 \leq x \leq 4$ and $- 3 < x < 3$
So domain of $f$ is $[2, 3)$

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