Find the domain of the function \( f(x) = \cos^{-1}(x^2 - 4) \).
Find the domain of the function \( f(x) = \cos^{-1}(x^2 - 4) \).
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Solution and Explanation
Top Questions on Functions
- If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
Give reasons to support your answer to (i).- Assertion (A): Let \( A = \{ x \in \mathbb{R} : -1 \leq x \leq 1 \} \). If \( f : A \to A \) be defined as \( f(x) = x^2 \), then \( f \) is not an onto function.
Reason (R): If \( y = -1 \in A \), then \( x = \pm \sqrt{-1} \notin A \). - If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$
- A real valued function $ f: A \to B $ defined by $ f(x) = \frac{4 - x^2}{4 + x^2} \ \forall x \in A $ is a bijection. If $ -4 \in A $, then $ A \cap B = $
Questions Asked in CBSE CLASS XII exam
Inspired by the success of Chandrayaan-3, the Chief Scientist at ‘Space Rover’ a private research group, decided to send some innovative ideas regarding the mission to the Chief Scientist of Chandrayaan-3. The Chief Scientist at ‘Space Rover’ formed four groups for the same. As it was an intellectual activity of thinking rather than doing, these four groups started interacting with each other and friendships developed. On the basis of their interaction and friendship, some members from each group formed ‘Entertainment Through Reading’ group which showed conformity in terms of their interest. ‘Entertainment Through Reading’ group had no written rules, was unstable in form and scope and had no fixed lines of communication. The members of this group enhanced the morale of each other, enjoyed drinking coffee together, read books, served different issues of their work areas and provided support to each other. Ultimately this group developed some innovative ideas which were sent by ‘Space Rover’ to the Chief Scientist of Chandrayaan-3. Though this group was formed for recreation but it contributed towards fulfillment of organisational objectives.
(a) Identify the function of management. Quoting the lines from the above para, explain the steps of the process of the function of management discussed.
(b) Also explain any two points of importance of the function of management identified in (a).- CBSE CLASS XII - 2025
- Controlling
(a) Identify and explain the function of management discussed in the above para.
(b) Explain any four points of importance of the function identified in (a).- CBSE CLASS XII - 2025
- Organizing
Explain the following factors affecting the working capital requirements of a business:
(i) Credit allowed
(ii) Production cycle
(iii) Availability of raw material- CBSE CLASS XII - 2025
- Financial Management and Financial Market
Explain the following points of significance of principles of management:
(i) Providing managers with useful insights into reality
(ii) Meeting changing environment requirements
(iii) Scientific decisions- CBSE CLASS XII - 2025
- Principles of Management
- Explain the following functions of marketing:
(i) Gathering and Analysing Market Information
(ii) Marketing Planning- CBSE CLASS XII - 2025
- Marketing Management