A function f : R_+ → R (where R_+ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is : (A) one-one but not onto (B) onto but not one-one (C) both one-one and onto (D) neither one-one nor onto

MathsCBSE Class 12 · Board exam 2024, set 65/1/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2024: question 1

Set in the CBSE Class 12 board exam of 2024, paper 65/1/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQRelations and Functions

A function $f : R_{+} \to R$ (where $R_{+}$ is the set of all non-negative real numbers) defined by $f (x) = 4 x + 3$ is :

(A)one-one but not onto
(B)onto but not one-one
(C)both one-one and onto
(D)neither one-one nor onto

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 65/1/1.

Hints

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

Hint 1

Check whether $4 x_{1} + 3 = 4 x_{2} + 3$ forces $x_{1} = x_{2}$ .

Hint 2

What is the least value of $f (x)$ when $x \geq 0$ ?

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.

$f (x_{1}) = f (x_{2}) \Rightarrow 4 x_{1} + 3 = 4 x_{2} + 3 \Rightarrow x_{1} = x_{2}$ , so $f$ is one-one.
½ mark
For $x \geq 0$ , $f (x) \geq 3$ , so values such as $0$ in the codomain $R$ have no pre-image. Hence $f$ is not onto.
½ mark

Answer: (A) one-one but not onto

Where the marks are

Identifies one-one but not onto (1 mark)

Revise the chapter

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

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 paper2024 board paper, set 65/1/1: 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 2024: question 1

Hints

Step-by-step solution

Revise the chapter

More questions from Relations and Functions