Maths-
General
Easy

Question

If [x] denotes the integral part of x, then domain of the function f left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction plus s i n to the power of negative 1 end exponent invisible function application open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets is

  1. [0, 2)    
  2. [0, 2) – {1}    
  3. left parenthesis negative infinity comma 3 right parenthesis minus left curly bracket 12 right curly bracket    
  4. none of these    

The correct answer is: [0, 2) – {1}


    For f (x) to be defined
    table row cell open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets equals negative 10 comma 1 end cell row cell negative 1 less or equal than fraction numerator 3 x minus 2 over denominator 2 end fraction less than 2 rightwards double arrow negative 2 less or equal than 3 x minus 2 less than 4 end cell row cell 0 less or equal than 3 x less than 6 rightwards double arrow 0 less or equal than x less than 2 horizontal ellipsis left parenthesis A right parenthesis end cell end table
    table row cell 3 minus x greater or equal than 0 text end text text a end text text n end text text d end text text end text x not equal to 12 comma 3 end cell row cell x less than 3 text end text text a end text text n end text text d end text text end text x not equal to 12 horizontal ellipsis left parenthesis B right parenthesis end cell end table
    table row cell text end text text F end text text r end text text o end text text m end text text end text left parenthesis A right parenthesis text end text text a end text text n end text text d end text text end text left parenthesis B right parenthesis text end text text , end text text end text text w end text text e end text text end text text h end text text a end text text v end text text e end text text end text end cell row cell 0 less or equal than x less than 1 text end text text o end text text r end text text end text 1 less than x less than 2 end cell row cell therefore text end text text D end text text o end text text m end text text a end text text i end text text n end text text end text equals open square brackets 01 close parentheses union open parentheses 12 close parentheses equals open square brackets 02 close parentheses minus open curly brackets 1 close curly brackets end cell end table

    Related Questions to study

    General
    maths-

    The domain of the function f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction is

    The domain of the function f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction is

    maths-General
    General
    maths-

    The domain of definition of the function Error converting from MathML to accessible text.

    The domain of definition of the function Error converting from MathML to accessible text.

    maths-General
    General
    maths-

    Let f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R be a function defined as y equals f left parenthesis x right parenthesis text  and  end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

    Let f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R be a function defined as y equals f left parenthesis x right parenthesis text  and  end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

    maths-General
    parallel
    General
    maths-

    Statement - I : Let f(x) be a function such that f left parenthesis x minus 1 right parenthesis plus f left parenthesis x plus 1 right parenthesis equals square root of 2 f left parenthesis x right parenthesis for all x element of R then f is periodic
    Statement - II : There exists a function with period 8

    Statement - I : Let f(x) be a function such that f left parenthesis x minus 1 right parenthesis plus f left parenthesis x plus 1 right parenthesis equals square root of 2 f left parenthesis x right parenthesis for all x element of R then f is periodic
    Statement - II : There exists a function with period 8

    maths-General
    General
    maths-

    An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

    An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

    maths-General
    General
    maths-

    If the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1 is inscribed in square of side length a square root of 2 comma then a is

    If the ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1 is inscribed in square of side length a square root of 2 comma then a is

    maths-General
    parallel
    General
    maths-

    The area of the quadrilateral formed by the tangents at the ends of latus-rectum of 5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45 is

    The area of the quadrilateral formed by the tangents at the ends of latus-rectum of 5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45 is

    maths-General
    General
    maths-

    In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is square root of 10 minus square root of 5 The equation of the ellipse

    In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is square root of 10 minus square root of 5 The equation of the ellipse

    maths-General
    General
    chemistry-

    Three metal ions x+2, y+2, z+2 are identify in qualitative analysis. Nitrates of x+2, y+2, z+2 dissolve in three seprate test tubes and gives following observation.
    i) All solution produce carbonate precipitate with (NH4 )2CO3
    ii) Only one produce white ppt on addition of NaCl.
    iii) Out of 3 cations two produce sulphide ppt.
    iv) Sulphide of y+2 is not produce by H2S/H+ but produce when H2S is passed in basic medium.
    v) Only y+2 produce soluble sulphate
    vi) x +2 gives no ppt with dil NH4OH
    Select correct about xCO3 , y CO3 , z CO3 -

    Three metal ions x+2, y+2, z+2 are identify in qualitative analysis. Nitrates of x+2, y+2, z+2 dissolve in three seprate test tubes and gives following observation.
    i) All solution produce carbonate precipitate with (NH4 )2CO3
    ii) Only one produce white ppt on addition of NaCl.
    iii) Out of 3 cations two produce sulphide ppt.
    iv) Sulphide of y+2 is not produce by H2S/H+ but produce when H2S is passed in basic medium.
    v) Only y+2 produce soluble sulphate
    vi) x +2 gives no ppt with dil NH4OH
    Select correct about xCO3 , y CO3 , z CO3 -

    chemistry-General
    parallel
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    Read the following comprehension carefully and answer the following questions

    chemistry-General
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    The compound

    Read the following comprehension carefully and answer the following questions

    The compound

    chemistry-General
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    Yellow solution (C) is an important laboratory reagent and is used in the estimation of :

    Read the following comprehension carefully and answer the following questions

    Yellow solution (C) is an important laboratory reagent and is used in the estimation of :

    chemistry-General
    parallel
    General
    chemistry-

    Read the following comprehension carefully and answer the following questions

    The colour of the ppt (D) & (E) are :

    Read the following comprehension carefully and answer the following questions

    The colour of the ppt (D) & (E) are :

    chemistry-General
    General
    chemistry-

    Moreover, the salt 'A' on heating with solid K2Cr2O7 and concentrated H2SO4 produces deep red vapours which dissolve in sodium hydroxide solution forming a yellow solution. This yellow solution gives yellow precipitate with Ba(NO3 ) 2 solution. On the basis of the aforesaid characteristic informations answer the following questions :
    Select the correct statement.

    Moreover, the salt 'A' on heating with solid K2Cr2O7 and concentrated H2SO4 produces deep red vapours which dissolve in sodium hydroxide solution forming a yellow solution. This yellow solution gives yellow precipitate with Ba(NO3 ) 2 solution. On the basis of the aforesaid characteristic informations answer the following questions :
    Select the correct statement.

    chemistry-General
    General
    chemistry-

    Statement-1 : Nessler’s reagent gives a brown precipitate with aqueous ammonia as well as with ammonium salts. Statement-2 : Aqueous ammonia gives a brown precipitate with a solution of manganese (II) chloride and hydrogen peroxide.

    Statement-1 : Nessler’s reagent gives a brown precipitate with aqueous ammonia as well as with ammonium salts. Statement-2 : Aqueous ammonia gives a brown precipitate with a solution of manganese (II) chloride and hydrogen peroxide.

    chemistry-General
    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.