Home
Class 12
MATHS
If a function f: R to R is defined as f...

If a function `f: R to R ` is defined as `f(x)=x^(3)+1`, then prove that f is one-one onto.

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1c|9 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1d|10 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1a|18 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.

Let f=NtoN be defined by f(x)=x^(2)+x+1,x inN , then prove that f is one-one but not onto.

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Prove that the function f: R^(+) to R which is defined as f(x)=log_(e) x is one - one .

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Show that the function f : R ->R , defined as f(x)=x^2 , is neither one-one nor onto.

Home
Profile