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If f left parenthesis x right parenthesis equals fraction numerator e to the power of x plus e to the power of negative x end exponent over denominator 2 end fraction ,then the inverse function of f left parenthesis x right parenthesis text  is  end text

Maths-General

  1. log subscript e invisible function application open parentheses x plus square root of x squared minus 1 end root close parentheses
  2. log subscript e invisible function application square root of x squared plus 1 end root
  3. log subscript e invisible function application open parentheses x plus square root of x squared plus 1 end root close parentheses
  4. log subscript e invisible function application open parentheses x minus square root of x squared minus 1 end root close parentheses

    Answer:The correct answer is: log subscript e invisible function application open parentheses x plus square root of x squared minus 1 end root close parentheses

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    General
    maths-

    If f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals

    If f left parenthesis x right parenthesis equals fraction numerator 10 to the power of x minus 10 to the power of negative x end exponent over denominator 10 to the power of x plus 10 to the power of negative x end exponent end fraction text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals

    maths-General
    General
    maths-

    Let f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket is given byf left parenthesis x right parenthesis equals 4 x cubed minus 3 x text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text  is given by  end text

    Let f colon open square brackets 1 half comma 1 close square brackets not stretchy rightwards arrow left square bracket negative 1 comma 1 right square bracket is given byf left parenthesis x right parenthesis equals 4 x cubed minus 3 x text  then  end text f to the power of negative 1 end exponent left parenthesis x right parenthesis text  is given by  end text

    maths-General
    General
    maths-

    If f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1 observe the following
    text  l)  end text delta f equals 2.11
    text  II)  end text d f equals 2.1
    text  III) Relative error in  end text x text  is  end text 1
    The true statements are

    If f left parenthesis x right parenthesis equals x squared plus x comma x equals 10 comma delta x equals 0.1 observe the following
    text  l)  end text delta f equals 2.11
    text  II)  end text d f equals 2.1
    text  III) Relative error in  end text x text  is  end text 1
    The true statements are

    maths-General
    General
    maths-

    Statement I :f colon A not stretchy rightwards arrow B text  is one - one and  end text g colon B not stretchy rightwards arrow C text  is a one-one function, then gof  end text colon A not stretchy rightwards arrow C is one - one
    Statement II :text  If  end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A are two functions such that g o f equals I subscript A text  and  end text fog equals I subscript B comma text  then  end text f equalsg to the power of negative 1 end exponent
    Staatement III : f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text  then  end text f equals g

    Which of the above statement/s is/are true.

    Statement I :f colon A not stretchy rightwards arrow B text  is one - one and  end text g colon B not stretchy rightwards arrow C text  is a one-one function, then gof  end text colon A not stretchy rightwards arrow C is one - one
    Statement II :text  If  end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A are two functions such that g o f equals I subscript A text  and  end text fog equals I subscript B comma text  then  end text f equalsg to the power of negative 1 end exponent
    Staatement III : f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text  then  end text f equals g

    Which of the above statement/s is/are true.

    maths-General
    General
    maths-

    The domain of the function  f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text  is  end text

    The domain of the function  f left parenthesis x right parenthesis equals fraction numerator tan invisible function application 2 x over denominator 6 cos invisible function application x plus 2 sin invisible function application 2 x end fraction text  is  end text

    maths-General
    General
    maths-

    2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals

    2.1 squared plus 3.2 squared plus 4.3 squared plus midline horizontal ellipsis horizontal ellipsis plus left parenthesis n plus 1 right parenthesis n squared equals

    maths-General
    General
    physics-

    A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 cross times 1 0 to the power of negative 5 end exponentm. The tube is immersed vertically into a liquid of surface tension 5.06 cross times 1 0 to the power of negative 2 end exponent N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

    P subscript i n end subscript equals P subscript 0 end subscript But P subscript 0 end subscript L equals P subscript i n end subscript open parentheses L minus x close parentheses

    A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 cross times 1 0 to the power of negative 5 end exponentm. The tube is immersed vertically into a liquid of surface tension 5.06 cross times 1 0 to the power of negative 2 end exponent N/m. To what length has the capillary to be immersed so that the liquid level inside and outside the capillary becomes the same?

    physics-General
    P subscript i n end subscript equals P subscript 0 end subscript But P subscript 0 end subscript L equals P subscript i n end subscript open parentheses L minus x close parentheses
    General
    physics-

    Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour

    Application of Bernoulli’s theorem

    Water flows through a frictionless duct with a cross-section varying as shown in fig. . Pressure p at points along the axis is represented by: A resume water to be non-viscour

    physics-General
    Application of Bernoulli’s theorem
    General
    physics-

    A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is 0.6 g c m to the power of negative 3 end exponent. The mass of block is

    Weight of block
    = Weight of displaced oil + Weight of displaced water
    Þ m g equals V subscript 1 end subscript rho subscript 0 end subscript g plus V subscript 2 end subscript rho subscript W end subscript g
    Þ m equals left parenthesis 10 cross times 10 cross times 6 right parenthesis cross times 0.6 plus left parenthesis 10 cross times 10 cross times 4 right parenthesis cross times 1= 760 gm

    A cubical block of wood 10 cm on a side floats at the interface between oil and water with its lower surface horizontal and 4 cm below the interface. The density of oil is 0.6 g c m to the power of negative 3 end exponent. The mass of block is

    physics-General
    Weight of block
    = Weight of displaced oil + Weight of displaced water
    Þ m g equals V subscript 1 end subscript rho subscript 0 end subscript g plus V subscript 2 end subscript rho subscript W end subscript g
    Þ m equals left parenthesis 10 cross times 10 cross times 6 right parenthesis cross times 0.6 plus left parenthesis 10 cross times 10 cross times 4 right parenthesis cross times 1= 760 gm
    General
    physics

    A particle is thrown in upward direction with initial velocity V0 It crosses point P at height  h at time t1 and t2 so t1 t2 ……..

    A particle is thrown in upward direction with initial velocity V0 It crosses point P at height  h at time t1 and t2 so t1 t2 ……..

    physicsGeneral
    General
    physics-

    Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

    When cross-section of duct is decreased, the velocity of water increased and in accordance with Bernoulli’s theorem, the pressure P decreased at that place

    Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by

    physics-General
    When cross-section of duct is decreased, the velocity of water increased and in accordance with Bernoulli’s theorem, the pressure P decreased at that place
    General
    physics-

    The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like

    When we move from centre to circumference, the velocity of liquid goes on decreasing and finally becomes zero

    The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like

    physics-General
    When we move from centre to circumference, the velocity of liquid goes on decreasing and finally becomes zero
    General
    maths-

    f colon R to the power of plus not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals log subscript e invisible function application x comma x element of left parenthesis 0 comma 1 right parenthesis comma f left parenthesis x right parenthesis equals 2 log subscript e invisible function application x comma x element of left square bracket 1 comma straight infinity right parenthesis text  is  end text

    f colon R to the power of plus not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals log subscript e invisible function application x comma x element of left parenthesis 0 comma 1 right parenthesis comma f left parenthesis x right parenthesis equals 2 log subscript e invisible function application x comma x element of left square bracket 1 comma straight infinity right parenthesis text  is  end text

    maths-General
    General
    maths-

    f colon R to the power of plus not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals 2 to the power of x comma x element of left parenthesis 0 comma 1 right parenthesis comma f left parenthesis x right parenthesis equals 3 to the power of x comma x element of left square bracket 1 comma straight infinity right parenthesis text  is  end text

    f colon R to the power of plus not stretchy rightwards arrow R text  defined by  end text f left parenthesis x right parenthesis equals 2 to the power of x comma x element of left parenthesis 0 comma 1 right parenthesis comma f left parenthesis x right parenthesis equals 3 to the power of x comma x element of left square bracket 1 comma straight infinity right parenthesis text  is  end text

    maths-General
    General
    physics-

    A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the

    A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the

    physics-General