Home
Class 12
MATHS
Show that , the function f: RR rarr RR d...

Show that , the function `f: RR rarr RR` defined by `f(x) =x^(3)+x` is bijective, here `RR` is the set of real numbers.

Text Solution

Verified by Experts

The correct Answer is:
hence it is bijective
Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|12 Videos

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( very short answer type questions)|22 Videos

  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos

  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

Let the function f:RR rarr RR be defined by f(x)=x^(2) (RR being the set of real numbers), then f is __

Find the image set of the domain of each of the following functions : g:RR to RR defined by, g(x) = x^2+2, for all x in RR, where RR is the set of real numbers.

The largest domain on which the function f: RR rarr RR defined by f(x)=x^(2) is ___

Discuss the bijectivity of the following mapping : f: RR rarr RR defined by f (x) = ax^(3) +b,x in RR and a ne 0' RR being the set of real numbers

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

Let the function f:RR rarr RR be defined by , f(x)=3x-2 and g(x)=3x-2 (RR being the set of real numbers), then (f o g)(x)=

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let A=RR-{2} and B=RR-{1} . Show that, the function f:A rarr B defined by f(x)=(x-3)/(x-2) is bijective .

Show that, the mapping f: RR rarr RR defined by f(x)=mx +n , where m,n, x in RR and m ne 0 , is a bijection.