Domain of the function: ^-1(2x) is (A) (-∞,∞) (B) (-1/2,1/2 ) (C) (-∞,-1/2 ) (1/2,∞ ) (D) (-∞,-1/2 ] [1/2,∞ )

MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2026-27: question 2

From the official CBSE sample question paper for 2026-27, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQInverse Trigonometric Functions

Domain of the function: $sec^{- 1} (2 x)$ is

(A) $(- \infty, \infty)$
(B) $(- \frac{1}{2}, \frac{1}{2})$
(C) $(- \infty, - \frac{1}{2}) \cup (\frac{1}{2}, \infty)$
(D) $(- \infty, - \frac{1}{2}] \cup [\frac{1}{2}, \infty)$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Recall the domain of $sec^{- 1} t$ .

Hint 2

Replace $t$ by $2 x$ and solve the 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.

$sec^{- 1} t$ is defined only for $∣ t ∣ \geq 1$ . So we need $∣2 x ∣ \geq 1$ , which gives $∣ x ∣ \geq \frac{1}{2}$ .
1 mark
Domain $= (- \infty, - \frac{1}{2}] \cup [\frac{1}{2}, \infty)$ .

Answer: Option (D)

Where the marks are

Uses $∣2 x ∣ \geq 1$ to get the domain (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 2026-27: every question, by section.

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CBSE Class 12 Mathematics sample paper 2026-27: question 2

Hints

Step-by-step solution

Revise the chapter

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