CBSE Class 12 Mathematics 2022 — QuizCluster Solutions
Comprehensive question-by-question independently authored solutions for CBSE Class 12 Mathematics Board Examination (2022). Questions are referenced directly to the official CBSE Question Paper.
Solutions and conceptual explanations are independently prepared by QuizCluster. QuizCluster is an independent educational platform and is not affiliated with, endorsed by, or sponsored by the Central Board of Secondary Education (CBSE). Official question papers are accessed via direct external links to official CBSE repositories and are never hosted or mirrored on QuizCluster.
Question Index
Q1 of 14Practice chapter-wise adaptive MCQs to strengthen weak concepts from this board paper.
View all years for this subjectDomain of Inverse Trigonometric Functions
Step 1: Domain condition for principal arcsine
The principal inverse sine function sin⁻¹(u) is defined if and only if -1 ≤ u ≤ 1. Here, u = 2x - 3.
Step 2: Solve the compound linear inequality
-1 ≤ 2x - 3 ≤ 1 Add 3 across all parts: -1 + 3 ≤ 2x ≤ 1 + 3 2 ≤ 2x ≤ 4 Divide by 2: 1 ≤ x ≤ 2.
- Domain of sin⁻¹(u): -1 ≤ u ≤ 1
- Range of sin⁻¹(u): [-π/2, π/2]
The argument inside any inverse sine or cosine function must always lie in the closed interval [-1, 1].
Forgetting to add 3 to both the left and right boundary values.
Source of question paper: Central Board of Secondary Education (CBSE). QuizCluster provides independently prepared educational solutions and explanations. QuizCluster is an independent educational platform and is not affiliated with or endorsed by CBSE. Question papers are accessed through links to official CBSE resources and are not hosted by QuizCluster.