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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Mathematics
Chapter
Functions

BITSAT 2015 · Mathematics · Functions

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

The domain of the function f(x)=sin⁡−1(x−3)9−x2f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}

Options

  1. A[1,2]
  2. B[2,3)
  3. C[1,2]
  4. D[2,3]

Correct answer

B. [2,3)

Step-by-step solution

f(x)=sin⁡−1(x−3)9−x2f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}} is defined if (i) −1≤x−3≤1⇒2≤x≤4-1 \leq x-3 \leq 1 \Rightarrow 2 \leq x \leq 4 and (ii) 9−x2>0⇒−3<x<39-x^{2} > 0 \Rightarrow-3< x< 3 Taking common solution of (i) and (ii), we get 2≤x<3∴2 \leq x< 3\therefore Domain =[2,3)=[2,3)
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