Home
Class 12
MATHS
Let A={x:-1 le x le 1}=B be a function f...

Let `A={x:-1 le x le 1}=B` be a function `f: A to B.` Then find the nature of each of the following functions.
(i) `f(x) = |x| " (ii) " f(x)=x|x|`
(iii) `f(x)=x^(3) " (iv) " f(x)="sin"(pi x)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
(i) Neither injecitve nor surjective (ii) bijective (iii) bijective (iv) many-one-into (v) bijective
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|6 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Check the nature of the following function. (i) f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N

Discuss the extrema of the following functions (i)f(x)=|x|,(ii)f(x)=e^(-|x|),(iii) f(x)=x^(2//3)

Find the range of each of the following functions: f(x)=|x-3| f(x)=1-|x-2| f(x)=(|x-4|)/(x-4)

Find the domain and range of the following functions. (i) f(x)=sqrt(2x-3) " (ii) " f(x) =(1)/(x-2) (iii) f(x) =x^(2) +3 " (iv) " f(x)=(1)/(x^(2)+2)

Prove the each of the following function is differentiable at x=0. (i) f(x) = cos|x| (ii) f(x) = x|x| (iii) f(x)=|x^(3)|(iv) f(x) =(x)/(1+|x|)

Find the domain of each of the following functions: f(x)=sin^(-1)x^2 (ii) f(x)=sin^(-1)x+sinx

Find the range of the following functions given by f(x)=(3)/(2-x^(2)) " " (ii) f(x)=1-|x-2| (iii) f(x)=|x-3| " " (iv) f(x)=1+3 cos 2x

Find the range of each of the following functions: f(x)=1/(sqrt(x-5)) (ii) f(x)=sqrt(6-x^2) (iii) f(x)=x/(1-x^2) (iv) f(x)=3/(2-x^2)

Separate the intervals of concavity of the following functions (i) f(x)= sin^(-1)x ,(ii) f(x)=x+sinx

Find the domain of each of the following functions given by f(x)=1/(sqrt(x-|x|)) (ii) f(x)=1/(sqrt(x+|x|)) (iii) f(x)=1/(sqrt(x-[x])) (iv) f(x)=1/(sqrt(x+[x]))