MathsCBSE Class 12 · Board exam 2023, set 65/1/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2023: question 21(a)

Set in the CBSE Class 12 board exam of 2023, paper 65/1/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerRelations and Functions

A function $f : A \to B$ defined as $f (x) = 2 x$ is both one-one and onto. If $A = {1, 2, 3, 4}$ , then find the set B.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/1/1.

Hints

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

Hint 1

For an onto function, the codomain equals the range.

Hint 2

Apply $f (x) = 2 x$ to each element of $A$ .

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.

Find the image of each element of $A$ under $f (x) = 2 x$ : $f (1) = 2, f (2) = 4, f (3) = 6, f (4) = 8$ .
1½ marks
Since $f$ is onto, every element of $B$ is an image. So $B$ is exactly the range: $B = {2, 4, 6, 8}$ .
½ mark

Answer: $B = {2, 4, 6, 8}$

Where the marks are

Computes $f (1), f (2), f (3), f (4)$ correctly (1½ marks)
Uses ontoness to conclude $B = {2, 4, 6, 8}$ (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Relations and Functions, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2023: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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