Find the domain of ^-1(3x-2)

MathsCBSE Class 12 · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2025-26: question 21(B)

From the official CBSE sample question paper for 2025-26, 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 $cos^{- 1} (3 x - 2)$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

What values can the argument of $cos^{- 1}$ take?

Hint 2

Put $3 x - 2$ between $- 1$ and $1$ and solve the double inequality.

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.

$cos^{- 1} t$ is defined only for $- 1 \leq t \leq 1$ , so we need $- 1 \leq 3 x - 2 \leq 1$ .
½ mark
Adding 2 throughout: $1 \leq 3 x \leq 3$ .
½ mark
Dividing by 3: $\frac{1}{3} \leq x \leq 1$ .
½ mark
Hence the domain of $cos^{- 1} (3 x - 2)$ is $[\frac{1}{3}, 1]$ .
½ mark

Answer: $[\frac{1}{3}, 1]$

Where the marks are

Writes the condition $- 1 \leq 3 x - 2 \leq 1$ (½ mark)
Simplifies to $1 \leq 3 x \leq 3$ (½ mark)
Gets $\frac{1}{3} \leq x \leq 1$ (½ mark)
States the domain as $[1/3, 1]$ (½ 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 2025-26: 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 2025-26: question 21(B)

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions