Identify the function shown in the graph (A) ^-1 x (B) ^-1(2x) (C) ^-1 (x/2 ) (D) 2^-1 x

MathsCBSE Class 12 · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2025-26: question 1

From the official CBSE sample question paper for 2025-26, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQInverse Trigonometric Functions

Identify the function shown in the graph

(A) $sin^{- 1} x$
(B) $sin^{- 1} (2 x)$
(C) $sin^{- 1} (\frac{x}{2})$
(D) $2 sin^{- 1} x$

Figure in the paper: Graph of an inverse trigonometric curve on X'OX, Y'OY axes, with y-values marked -π/2 to π/2 (dashed horizontal lines at ±π/2) and dashed vertical lines at the ends of the domain, which lies between about -0.5 and 0.5 (x=1 marked on axis); the curve is increasing, passing through the origin. See it in the official paper.

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

Read the domain from the dashed vertical lines.

Hint 2

For which option does the expression inside $sin^{- 1}$ reach $\pm 1$ at $x = \pm \frac{1}{2}$ ?

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.

From the graph, the domain is $[- \frac{1}{2}, \frac{1}{2}]$ and the range is $[- \frac{π}{2}, \frac{π}{2}]$ ; the curve increases through the origin.
$sin^{- 1} (2 x)$ is defined when $- 1 \leq 2 x \leq 1$ , i.e. $- \frac{1}{2} \leq x \leq \frac{1}{2}$ , and its range is $[- \frac{π}{2}, \frac{π}{2}]$ . So the graph is of $sin^{- 1} (2 x)$ , option (B).
1 mark

Answer: $sin^{- 1} (2 x)$ , option (B)

Where the marks are

Matches the domain $[- \frac{1}{2}, \frac{1}{2}]$ to $sin^{- 1} (2 x)$ (1 mark)

Revise the chapter

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

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 1

Hints

Step-by-step solution

Revise the chapter

More questions from Inverse Trigonometric Functions