Home
Class 12
MATHS
If f:RtoR,defined by F(x)=1+x^2, then sh...

If `f:RtoR,`defined by `F(x)=1+x^2`, then show that f is neither 1 - 1 nor onto.

Text Solution

Verified by Experts

The correct Answer is:
`therefore` f is not onto.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • II PUC MARCH - 2017

    OSWAAL PUBLICATION|Exercise PART - C|14 Videos

  • II PUC MARCH - 2017

    OSWAAL PUBLICATION|Exercise PART - D|9 Videos

  • II PUC MARCH - 2017

    OSWAAL PUBLICATION|Exercise PART - E|3 Videos

  • II PUC JULY -2016

    OSWAAL PUBLICATION|Exercise PART-E (V. Answer any ten questions : )|3 Videos

  • II PUC MARCH-2016

    OSWAAL PUBLICATION|Exercise PART - E|2 Videos

Similar Questions

Explore conceptually related problems

If f : R to R defined by f(x) = 1+x^(2), then show that f is neither 1-1 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.

Knowledge Check

  • If f:RtoR is defined by f(x)=x^(3) then f^(-1)(8)=

    A
    `{2,-2}`
    B
    `{2,2}`
    C
    `{2}`
    D
    `{2,omega,2omega^(2)}`

  • Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

    A
    one-one, onto
    B
    many one onto
    C
    one-one but not onto
    D
    onto but not one-one

    • Similar Questions

    Explore conceptually related problems

    If f:RrarrR defined by f(x)=(4x+3) , show that f is invertible and find f^(-1 .

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

    Show that the function f : R to R defined by f(x) = x^(2) AA x in R is neither injective nor subjective.

    If f : R to R is defined by f (x) = 2x + 3 , then f^(-1) x

    f : R to R be defined as f(x) = 4x + 5 AA x in R show that f is invertible and find f^(-1) .

    If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

    Home
    Profile