Match each function in List I with its description in List II.

Match each function in List I with its…

Question 116

HardOriginal question

Match each function in List I with its description in List II.

List I	List II
A. $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = 2x + 1$	I. One-one but not onto
B. $f : \mathbb{N} \to \mathbb{N}$ , $f(n) = 3n$	II. Neither one-one nor onto
C. $f : \mathbb{R} \to [0, \infty)$ , $f(x) = \lvert x \rvert$	III. One-one and onto
D. $f : \mathbb{R} \to \mathbb{R}$ , $f(x) = x^{2} + 1$	IV. Onto but not one-one

A-I, B-III, C-IV, D-IICorrect answerYour answerA-III, B-I, C-IV, D-IICorrect answerYour answerA-III, B-I, C-II, D-IVCorrect answerYour answerA-I, B-III, C-II, D-IVCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$2x + 1$ is a bijection of $\mathbb{R}$ ; $3n$ is one-one but misses 1 and 2.
$\lvert x \rvert$ onto $[0, \infty)$ repeats $\pm x$ ; $x^{2} + 1$ repeats and never reaches 0.

Concept: Matching functions to their type
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsOnto and bijective functions

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.

Question 116

Explanation