Maths-
General
Easy

Question

Domain of definition of the function f left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x squared end fraction plus log subscript 10 invisible function application open parentheses x cubed minus x close parentheses comma text  is  end text

  1. left parenthesis 1 comma 2 right parenthesis
  2. left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis
  3. left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma straight infinity right parenthesis
  4. left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma straight infinity right parenthesis

The correct answer is: left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma straight infinity right parenthesis


    Since, f left parenthesis x right parenthesis equals fraction numerator 3 over denominator 4 minus x squared end fraction plus log subscript 10 invisible function application open parentheses x cubed minus x close parentheses
    For domain of f left parenthesis x right parenthesis
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell open x cubed minus 1 greater than 0 comma 4 minus x squared not equal to 0 close parentheses end cell row cell not stretchy rightwards double arrow x left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis greater than 0 text  and  end text x not equal to plus-or-minus 2 end cell row cell not stretchy rightwards double arrow x element of left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma straight infinity right parenthesis comma x not equal to plus-or-minus 2 end cell end table


    not stretchy rightwards double arrow x element of left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma straight infinity right parenthesis

    Related Questions to study

    General
    maths-

    text  If  end text f left parenthesis x right parenthesis equals open parentheses fraction numerator x over denominator 1 minus vertical line x vertical line end fraction close parentheses to the power of 1 divided by 2002 end exponent comma text  then  end text D subscript f text  is  end text

    text  If  end text f left parenthesis x right parenthesis equals open parentheses fraction numerator x over denominator 1 minus vertical line x vertical line end fraction close parentheses to the power of 1 divided by 2002 end exponent comma text  then  end text D subscript f text  is  end text

    maths-General
    General
    maths-

    Range of the function f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text  is  end text

    Range of the function f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text  is  end text

    maths-General
    General
    maths-

    Range of the function f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text  is  end text

    Range of the function f left parenthesis x right parenthesis equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction semicolon x element of R text  is  end text

    maths-General
    parallel
    General
    maths-

    The domain of  sin to the power of negative 1 end exponent invisible function application open parentheses log subscript 3 invisible function application x close parentheses text  is  end text

    The domain of  sin to the power of negative 1 end exponent invisible function application open parentheses log subscript 3 invisible function application x close parentheses text  is  end text

    maths-General
    General
    maths-

    The domain of the function  f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript invisible function application open parentheses x squared minus 1 close parentheses text  is  end text

    The domain of the function  f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript invisible function application open parentheses x squared minus 1 close parentheses text  is  end text

    maths-General
    General
    Maths-

    If f left parenthesis x right parenthesis equals 2 x to the power of 6 plus 3 x to the power of 4 plus 4 x squared , then f to the power of straight prime left parenthesis x right parenthesis is

    Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.

    If f left parenthesis x right parenthesis equals 2 x to the power of 6 plus 3 x to the power of 4 plus 4 x squared , then f to the power of straight prime left parenthesis x right parenthesis is

    Maths-General

    Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables. A constant function has zero derivatives. For instance, f'(x) = 0 if f(x) = 8. So the derivative function is odd.

    parallel
    General
    maths-

    The domain of the function f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses is

    The domain of the function f left parenthesis x right parenthesis equals log subscript 2 invisible function application open parentheses log subscript 3 invisible function application open parentheses log subscript 4 invisible function application x close parentheses close parentheses is

    maths-General
    General
    maths-

    text  If  end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text  then, domain of  end text f left parenthesis x right parenthesis text  is  end text

    text  If  end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text  then, domain of  end text f left parenthesis x right parenthesis text  is  end text

    maths-General
    General
    maths-

    The domain of the function f left parenthesis x right parenthesis equals exp invisible function application open parentheses square root of 5 x minus 3 minus 2 x squared end root close parentheses is

    The domain of the function f left parenthesis x right parenthesis equals exp invisible function application open parentheses square root of 5 x minus 3 minus 2 x squared end root close parentheses is

    maths-General
    parallel
    General
    maths-

    The value of  tan invisible function application open curly brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 2 over 7 close parentheses minus pi over 2 close curly brackets is

    The value of  tan invisible function application open curly brackets cos to the power of negative 1 end exponent invisible function application open parentheses negative 2 over 7 close parentheses minus pi over 2 close curly brackets is

    maths-General
    General
    maths-

    sin invisible function application open parentheses 1 half cos to the power of negative 1 end exponent invisible function application 4 over 5 close parentheses is equal to

    sin invisible function application open parentheses 1 half cos to the power of negative 1 end exponent invisible function application 4 over 5 close parentheses is equal to

    maths-General
    General
    maths-

    If a greater than b greater than 0 , then the value of  tan to the power of negative 1 end exponent invisible function application open parentheses a over b close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator a plus b over denominator a minus b end fraction close parentheses depends on

    If a greater than b greater than 0 , then the value of  tan to the power of negative 1 end exponent invisible function application open parentheses a over b close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator a plus b over denominator a minus b end fraction close parentheses depends on

    maths-General
    parallel
    General
    maths-

    cot to the power of negative 1 end exponent invisible function application left parenthesis square root of cos invisible function application alpha end root right parenthesis minus tan to the power of negative 1 end exponent invisible function application left parenthesis square root of cos invisible function application alpha end root right parenthesis equals x then is equal to

    cot to the power of negative 1 end exponent invisible function application left parenthesis square root of cos invisible function application alpha end root right parenthesis minus tan to the power of negative 1 end exponent invisible function application left parenthesis square root of cos invisible function application alpha end root right parenthesis equals x then is equal to

    maths-General
    General
    maths-

    Number of solutions of the equation  tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 2 x plus 1 end fraction close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 4 x plus 1 end fraction close parentheses equals tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses is

    Number of solutions of the equation  tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 2 x plus 1 end fraction close parentheses plus tan to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 4 x plus 1 end fraction close parentheses equals tan to the power of negative 1 end exponent invisible function application open parentheses 2 over x squared close parentheses is

    maths-General
    General
    maths-

    text  If  end text sec to the power of negative 1 end exponent invisible function application square root of 1 plus x squared end root plus cosec to the power of negative 1 end exponent invisible function application fraction numerator square root of 1 plus y squared end root over denominator y end fraction plus cot to the power of negative 1 end exponent invisible function application 1 over z equals pi text  then  end text x plus y plus z is equal to

    text  If  end text sec to the power of negative 1 end exponent invisible function application square root of 1 plus x squared end root plus cosec to the power of negative 1 end exponent invisible function application fraction numerator square root of 1 plus y squared end root over denominator y end fraction plus cot to the power of negative 1 end exponent invisible function application 1 over z equals pi text  then  end text x plus y plus z is equal to

    maths-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.