Maths-
General
Easy

Question

The function f colon R not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket comma straight for all x element of R text  is  end text

  1. one-one
  2. onto
  3. Both one-one and onto
  4. neither one-one nor onto

hintHint:

In this question, we have to find the type of function if f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line comma f colon left square bracket 2 comma 3 right square bracket not stretchy rightwards arrow R A function f colon A rightwards arrow B is said to be one-one if different elements of A have different images in B, a function f colon A rightwards arrow B is said to be onto if for all y element of B, there exists x element of A such that f (x) = y.

The correct answer is: neither one-one nor onto


    We have f(x)=x-[x].
    Clearly, f(x)=0 for all x element of Z.
    So, f(x) is not one-one function.
    Also, range= [0,1) not equal toR
    So, f(x) is not into function.

    Related Questions to study

    General
    physics-

    A sphere of radius ‘R’ floats in a liquid of density ‘s’ such that its diameter x-x is below distance ‘h’ from free surface as shown. The density of sphere is r. The sphere is depressed slightly and released. The frequency of small oscillation is

    A sphere of radius ‘R’ floats in a liquid of density ‘s’ such that its diameter x-x is below distance ‘h’ from free surface as shown. The density of sphere is r. The sphere is depressed slightly and released. The frequency of small oscillation is

    physics-General
    General
    Physics-

    A conical flask of mass 10 kg and base area as 103 cm2 is floating in liquid of relative density 1.2, as shown in the figure. The force that liquid exerts on curved surface of conical flask will be (Given g = 10 m/s2)

    A conical flask of mass 10 kg and base area as 103 cm2 is floating in liquid of relative density 1.2, as shown in the figure. The force that liquid exerts on curved surface of conical flask will be (Given g = 10 m/s2)

    Physics-General
    General
    Physics-

    A vertical jet of water coming out of a nozzle with velocity 20 m/s supports a plate of mass M stationary at a height h = 15m, as shown in the figure. If the rate of water flow is 1 litre per second, the mass of the plate is (Assume the collision to be inelastic).

    A vertical jet of water coming out of a nozzle with velocity 20 m/s supports a plate of mass M stationary at a height h = 15m, as shown in the figure. If the rate of water flow is 1 litre per second, the mass of the plate is (Assume the collision to be inelastic).

    Physics-General
    parallel
    General
    physics-

    A thin movable plate is separated from two fixed plates P subscript 1 and P subscript 2 by two highly viscous liquids of coefficients of viscosity n subscript 1 and n subscript 2 as shown, where n subscript 2 end subscript equals 9 n subscript 1 end subscript. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is ‘h’, then the distance ‘h subscript 1 end subscript’ of movable plate from upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is ( assume only linear velocity distribution in each liquid).

    A thin movable plate is separated from two fixed plates P subscript 1 and P subscript 2 by two highly viscous liquids of coefficients of viscosity n subscript 1 and n subscript 2 as shown, where n subscript 2 end subscript equals 9 n subscript 1 end subscript. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is ‘h’, then the distance ‘h subscript 1 end subscript’ of movable plate from upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is ( assume only linear velocity distribution in each liquid).

    physics-General
    General
    physics-

    Figure shows a stream of fluid emerging from a tube in the base of an open fixed tank. The expression of ‘y’ (Maximum height traveled by jet of water) is

    Figure shows a stream of fluid emerging from a tube in the base of an open fixed tank. The expression of ‘y’ (Maximum height traveled by jet of water) is

    physics-General
    General
    physics-

    For the arrangement shown in figure the time interval after which the water jet ceases to cross the wall (area of cross section of tank is A and orifice is ‘a’)

    For the arrangement shown in figure the time interval after which the water jet ceases to cross the wall (area of cross section of tank is A and orifice is ‘a’)

    physics-General
    parallel
    General
    physics

    The distance travelled by a particle is given by S=3+2t +5t2The initial velocity of the particle is…..

    The distance travelled by a particle is given by S=3+2t +5t2The initial velocity of the particle is…..

    physicsGeneral
    General
    maths-

    If f colon R not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals x squared minus 2 x minus 3 text  then  end text f text  is  end text

    If f colon R not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals x squared minus 2 x minus 3 text  then  end text f text  is  end text

    maths-General
    General
    physics

    A freely falling particle covers a building of 45 m height in one second. Find the height of the point from where the particle was released.[g=10 ms-2]

    A freely falling particle covers a building of 45 m height in one second. Find the height of the point from where the particle was released.[g=10 ms-2]

    physicsGeneral
    parallel
    General
    physics

    The displacement of a particle in x direction is given by x.=9-5t+4t2 Find the Velocity at time t=0

    The displacement of a particle in x direction is given by x.=9-5t+4t2 Find the Velocity at time t=0

    physicsGeneral
    General
    Maths-

    If f colon left square bracket 0 comma 1 right square bracket not stretchy rightwards arrow left square bracket negative 1 comma 3 right square bracket defined by f left parenthesis x right parenthesis equals x squared plus x plus 1 text , then  end text f text  is  end text

    If f colon left square bracket 0 comma 1 right square bracket not stretchy rightwards arrow left square bracket negative 1 comma 3 right square bracket defined by f left parenthesis x right parenthesis equals x squared plus x plus 1 text , then  end text f text  is  end text

    Maths-General
    General
    Maths-

    If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line comma f colon left square bracket 2 comma 3 right square bracket not stretchy rightwards arrow R text  is  end text

    If f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line comma f colon left square bracket 2 comma 3 right square bracket not stretchy rightwards arrow R text  is  end text

    Maths-General
    parallel
    General
    physics-

    Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are

    Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are

    physics-General
    General
    maths-

    A equals left curly bracket x colon negative 1 less or equal than x less or equal than 1 right curly bracket. f colon A not stretchy rightwards arrow A defined by f left parenthesis x right parenthesis equals x vertical line x vertical linetext  Then  end text f text  is  end text

    A equals left curly bracket x colon negative 1 less or equal than x less or equal than 1 right curly bracket. f colon A not stretchy rightwards arrow A defined by f left parenthesis x right parenthesis equals x vertical line x vertical linetext  Then  end text f text  is  end text

    maths-General
    General
    physics

    What does the speedometer measure kept in motorbike ?

    What does the speedometer measure kept in motorbike ?

    physicsGeneral
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.