Home
Class 12
MATHS
Which of the following function is surje...

Which of the following function is surjective but not injective?

A

`f:RrarrR, f(x)=x^(4)+2x^(3)-x^(2)+1`

B

`f:RrarrR,f(x)=x^(3)+x+1`

C

`f:RrarrR,f(x)=sqrt(1+x^(2))`

D

`f:RrarrR, f(x)=x^(3)+2x^(2)-x+1`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=x^(4)+2x^(3)-x^(2)+1` is polynomial of even degree hence its range can't be R.
hence not surjective
`f(x)=x^(3) =x^(3)+x+1,f'(x)=3x^(2)+1`
implies monotonic hence bijective.
`f(x) -sqrt(1+x^(2)),`
neither surjective not injective.
`f(x)=x^(3)+2x^(2)-x+1`
`f'(x)=3x^(2)+4x-1 implies D=16+12gt0`.
Hence f(x) is non-monotonic cubic polynomial hence surjective but not injective
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If co-domain is R, then which of the following functions is not a surjective (onto) function?

Classify the following functions as injective, surjective, both or none.DRbbe a function defined by X)f:Rvec R, be a function defined by f(x)= - + 48 73072 – 8x + 18fRRbe a function defined by f(x)=v3 62

Knowledge Check

  • Which of the following functions is injective ?

    A
    `f(x)=x^(2)+3, x in (-oo, oo)`
    B
    `f(x)=|x+1|, x in [2, oo)`
    C
    `f(x)=(x-4)(x-5), x in (oo, 5]`
    D
    `f(x)=(4x^(2)+3x-5)/(4+3x+5x^(2)), x in (-oo, oo)`

  • Which of the following functions is a surjection?

    A
    `f:R to R" given by "f(x)=x^(3)+2"for all x"in R`
    B
    `g:R to R" given by "g(x)=x^(2)+2"for all x"in R`
    C
    `h:Z to Z" given by "h(x)=3x+2"for all x"in Z`
    D
    `phi: R to R" given by "f(x)=x^(2)-3x+2"for all x"in R`

  • Which one of the following functions f:RtoR is injective?

    A
    `f(x)=|x|" for all "x""inR`
    B
    `f(x)=x^(2)" for all "x""inR`
    C
    `f(x)=11" for all "x""inR`
    D
    `f(x)=-x" for all "x""inR`

    • Similar Questions

    Explore conceptually related problems

    Let R be the set of real numbers.If f:R rarr R is a function defined by f(x)=x^(2), then f is injective but not surjective surjective but not injective but not surjective surjective but not but not surjective (b) surjective but not injective (c) bijective (d) non of these

    Classify the following function f(x) defined in RtoR as injective, surjective, both or none. f(x)=x|x|

    Classify the following function f(x) defined in RtoR as injective, surjective, both or none. f(x)=(x^(2))/(1+x^(2))

    Let D-=[-1,1] is the domain of the following functions state which of them are injective.

    In which of the following preformed antibodies are directly injected into the body

    Home
    Profile