Find the domain of ^-1(x²-4).

MathsCBSE Class 12 · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2023-24: question 21(b)

From the official CBSE sample question paper for 2023-24, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(b) · 2 marks · Very short answerInverse Trigonometric Functions

Find the domain of $sin^{- 1} (x^{2} - 4)$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

What values may the input of $sin^{- 1}$ take?

Hint 2

Solve $3 \leq x^{2} \leq 5$ , remembering that $x$ can be negative.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$sin^{- 1} t$ is defined only for $- 1 \leq t \leq 1$ . So $- 1 \leq x^{2} - 4 \leq 1 \Rightarrow 3 \leq x^{2} \leq 5 \Rightarrow 3 \leq ∣ x ∣ \leq 5$ .
1 mark
So $x \in [- 5, - 3] \cup [3, 5]$ , and this is the domain.
1 mark

Answer: $[- 5, - 3] \cup [3, 5]$

Where the marks are

Sets $- 1 \leq x^{2} - 4 \leq 1$ and gets $3 \leq ∣ x ∣ \leq 5$ (1 mark)
Writes the domain as a union of intervals (1 mark)

Revise the chapter

Chapter: Inverse Trigonometric Functions (notes, formulas, where marks are lost and every past question)
Topic: Domain and Range of Inverse Trigonometric Functions

Practise this chapterBoard-style questions from Inverse Trigonometric Functions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Mathematics sample paper 2023-24: question 21(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions