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

JEE Main · 2004 · 24 Apr 2004 · Offline · Inverse Trigonometric Functions

The domain of the function

f (x) = \frac{s i n ^{- 1} ( x - 3 )}{9 - x ^{2}}

Answer: (B)

Two conditions must hold together. For

sin^{- 1} (x - 3)

the argument needs

- 1 \leq x - 3 \leq 1

, i.e.

2 \leq x \leq 4

. For

9 - x^{2}

in the denominator we need

9 - x^{2} > 0

, strictly, since it cannot be zero, i.e.

- 3 < x < 3

. The overlap of

[2, 4]

and

(- 3, 3)

[2, 3)

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