Discussion
Let \(f(x) = \sin^{-1}x\) and \(g(x) = x - 2\). To define the composite function \(f \circ g\), the largest domain of \(g(x)\) has to be
Answer: B
The largest domain is \([1, 3]\).
\(f(g(x)) = \sin^{-1}(x - 2)\), and \(\sin^{-1}\) is defined only for arguments between \(-1\) and \(1\).
\[ \begin{aligned} -1 &\le x - 2 \le 1 \\ 1 &\le x \le 3 \end{aligned} \]
The interval \([-1, 3]\) or \([-3, 3]\) would let \(x - 2\) fall below \(-1\), and \([2, 5]\) lets it exceed 1, so \(f \circ g\) would be undefined at some points. \([0, 2]\) works but is not the largest such interval.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development