(D) Given the function $f(x) = x - 5[\frac{x}{5}]$.To check for one-one: Calculate $f(1) = 1 - 5[1/5] = 1 - 5(0) = 1$ and $f(6) = 6 - 5[6/5] = 6 - 5(1

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Given the function $f(x) = x - 5[\frac{x}{5}]$.To check for one-one: Calculate $f(1) = 1 - 5[1/5] = 1 - 5(0) = 1$ and $f(6) = 6 - 5[6/5] = 6 - 5(1) = 1$.Since $f(1) = f(6) = 1$ but $1 \neq 6$,the function is not one-one.To check for onto: The codomain is $N = \{1, 2, 3, ...\}$.Calculate $f(5) = 5 - 5[5/5] = 5 - 5(1) = 0$.Since $0 \notin N$,the function is not onto.Therefore,the function $f$ is neither one-one nor onto.

Class 12 Mathematics Relation and Function Type of Functions based on Mapping

Difficult

The function $f : N \to N$ defined by $f(x) = x - 5[\frac{x}{5}]$,where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$,is

JEE MAIN 2017 All JEE MAIN

A
one-one and onto.
B
one-one but not onto.
C
onto but not one-one.
D
neither one-one nor onto.

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Relation and Function

Subtopic

Type of Functions based on Mapping

Previous Year

JEE MAIN 2017 Paper All JEE MAIN years →

Which of the following functions is injective but not surjective?

View Solution

Let $A = \{x : x \in R, x \text{ is not a positive integer}\}$. Define $f: A \rightarrow R$ as $f(x) = \frac{2x}{x-1}$. Then $f$ is:

EasyKCET 2021

View Solution

If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :

MediumAP EAMCET 2006

View Solution

Show that the function $f: R_* \rightarrow R_$ defined by $f(x) = \frac{1}{x}$ is one-one and onto,where $R_$ is the set of all non-zero real numbers. Is the result true if the domain $R_$ is replaced by $N$ with the co-domain remaining the same as $R_$?

Medium

View Solution

Which of the following statements is true?

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The function $f : N \to N$ defined by $f(x) = x - 5[\frac{x}{5}]$,where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$,is

Similar Questions

Which of the following functions is injective but not surjective?

Let $A = \{x : x \in R, x \text{ is not a positive integer}\}$. Define $f: A \rightarrow R$ as $f(x) = \frac{2x}{x-1}$. Then $f$ is:

If $f: R \rightarrow R$ is defined by $f(x)=x-[x]-\frac{1}{2}$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then $\{x \in R: f(x)=\frac{1}{2}\}$ is equal to :

Show that the function $f: R_* \rightarrow R_*$ defined by $f(x) = \frac{1}{x}$ is one-one and onto,where $R_*$ is the set of all non-zero real numbers. Is the result true if the domain $R_*$ is replaced by $N$ with the co-domain remaining the same as $R_*$?

Which of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Show that the function $f: R_* \rightarrow R_$ defined by $f(x) = \frac{1}{x}$ is one-one and onto,where $R_$ is the set of all non-zero real numbers. Is the result true if the domain $R_$ is replaced by $N$ with the co-domain remaining the same as $R_$?