Maths-
General
Easy

Question

If two real valued functions f(x) & g(x) are given, for fog(x), g(x) is substituted in place of x in f(x) taking care of the domain of fog(x) which is subset of Domain of g(x), only those values of x such that g(x) lies in the Domain of f. Now, If f left parenthesis x right parenthesis equals s i n to the power of 2 end exponent invisible function application x plus s i n to the power of 2 end exponent invisible function application open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses plus c o s invisible function application x times c o s invisible function application open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses text  and  end text g open parentheses fraction numerator 5 over denominator 4 end fraction close parentheses equals 1 then g of (x) is

  1. a polynomial of first degree in sin x, cos x    
  2. a constant function    
  3. a polynomial of second degree in sin x, cos x    
  4. none of these    

The correct answer is: a constant function


    f(x) = sin2x + sin2 open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses
    cosx . cos open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses
    = sin2x + open parentheses fraction numerator 1 over denominator 2 end fraction s i n invisible function application x plus fraction numerator square root of 3 over denominator 2 end fraction c o s invisible function application x close parentheses to the power of 2 end exponent
    cosx open parentheses c o s invisible function application x times fraction numerator 1 over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction s i n invisible function application x close parentheses= fraction numerator 5 over denominator 4 end fraction

    Related Questions to study

    General
    Maths-

    where x, y, t R If t (5, k], then greatest value of k for which x is one-one function of t is

    where x, y, t R If t (5, k], then greatest value of k for which x is one-one function of t is

    Maths-General
    General
    Maths-

    STATEMENT-I : If [4x] = [x], then the largest set of values of x is. open square brackets negative fraction numerator 1 over denominator 4 end fraction comma fraction numerator 1 over denominator 4 end fraction close parentheses and
    STATEMENT-II : If [nx] = [x], n element of I to the power of plus end exponent then the largest set of values of x is open square brackets negative fraction numerator 1 over denominator n end fraction comma fraction numerator 1 over denominator n end fraction close parentheses

    STATEMENT-I : If [4x] = [x], then the largest set of values of x is. open square brackets negative fraction numerator 1 over denominator 4 end fraction comma fraction numerator 1 over denominator 4 end fraction close parentheses and
    STATEMENT-II : If [nx] = [x], n element of I to the power of plus end exponent then the largest set of values of x is open square brackets negative fraction numerator 1 over denominator n end fraction comma fraction numerator 1 over denominator n end fraction close parentheses

    Maths-General
    General
    Maths-

    x to the power of 4 end exponent minus 4 x minus 1 equals 0 text end texthas

    x to the power of 4 end exponent minus 4 x minus 1 equals 0 text end texthas

    Maths-General
    parallel
    General
    Chemistry-

    ClCH2COOH is heated with fuming HNO3 in the presence of AgNO3 in carius tube After filtration and washing a white precipitate is obtained The precipitate is of

    ClCH2COOH is heated with fuming HNO3 in the presence of AgNO3 in carius tube After filtration and washing a white precipitate is obtained The precipitate is of

    Chemistry-General
    General
    Chemistry-

    Sodium extract gives blood red colour when treated with FeCl3 Formation of blood red colour confirms the presence of

    Sodium extract gives blood red colour when treated with FeCl3 Formation of blood red colour confirms the presence of

    Chemistry-General
    General
    Maths-

    STATEMENT-I : The graph ofblank y equals left square bracket square root of 1 minus c o s invisible function application 2 x end root right square bracket consists of only two line segments. Where [.] represent greatest integer function and
    STATEMENT-II : The graph ofblank y equals square root of 1 minus c o s invisible function application 2 x end root is

    STATEMENT-I : The graph ofblank y equals left square bracket square root of 1 minus c o s invisible function application 2 x end root right square bracket consists of only two line segments. Where [.] represent greatest integer function and
    STATEMENT-II : The graph ofblank y equals square root of 1 minus c o s invisible function application 2 x end root is

    Maths-General
    parallel
    General
    Maths-

    Statement 1: Letblank f colon left parenthesis a comma b right parenthesis rightwards arrow left square bracket c comma d right square bracket be a continuous and onto function, then it cannot be one-one. And
    Statement 2: If for a continuous and differentiable function f,blank f to the power of ´ end exponent left parenthesis x right parenthesis greater than 0 then f(x) is one-one

    Statement 1: Letblank f colon left parenthesis a comma b right parenthesis rightwards arrow left square bracket c comma d right square bracket be a continuous and onto function, then it cannot be one-one. And
    Statement 2: If for a continuous and differentiable function f,blank f to the power of ´ end exponent left parenthesis x right parenthesis greater than 0 then f(x) is one-one

    Maths-General
    General
    Maths-

    Number of solutions of the equation |3x 2| = 3[x] + 2{x}, where [.] and {.} denote the integral and fractional parts of x respectively, is

    Number of solutions of the equation |3x 2| = 3[x] + 2{x}, where [.] and {.} denote the integral and fractional parts of x respectively, is

    Maths-General
    General
    Chemistry-

    A mixture of benzene and toluene can be separated by

    A mixture of benzene and toluene can be separated by

    Chemistry-General
    parallel
    General
    Maths-

    The solution set of the inequality log1/5 (2x + 5) + log5 (16 x 2) 1 is

    The solution set of the inequality log1/5 (2x + 5) + log5 (16 x 2) 1 is

    Maths-General
    General
    Maths-

    Let f be an injective map with domainblank left curly bracket x comma y comma z right curly bracket and rangeblank left curly bracket 1 , 2 comma 3 right curly bracket such that exactly one of the following statements is correct and the remaining are falseblank f left parenthesis x right parenthesis equals 1 comma f left parenthesis y right parenthesis not equal to 1 comma f left parenthesis z right parenthesis not equal to 2 The value ofblank f to the power of negative 1 end exponent left parenthesis 1 right parenthesis blankis

    For such questions, we should know concept of injective function.

    Let f be an injective map with domainblank left curly bracket x comma y comma z right curly bracket and rangeblank left curly bracket 1 , 2 comma 3 right curly bracket such that exactly one of the following statements is correct and the remaining are falseblank f left parenthesis x right parenthesis equals 1 comma f left parenthesis y right parenthesis not equal to 1 comma f left parenthesis z right parenthesis not equal to 2 The value ofblank f to the power of negative 1 end exponent left parenthesis 1 right parenthesis blankis

    Maths-General

    For such questions, we should know concept of injective function.

    General
    Chemistry-

    Hyper conjugation effect is not possible in which of the following species

    Hyper conjugation effect is not possible in which of the following species

    Chemistry-General
    parallel
    General
    Maths-

    The graph (y x) againstblank left parenthesis y plus x comma y minus x right parenthesis is as shown. Which one of the following shows the graph of y against ?

    The graph (y x) againstblank left parenthesis y plus x comma y minus x right parenthesis is as shown. Which one of the following shows the graph of y against ?

    Maths-General
    General
    Maths-

    For each x in [0, 1] define f(x) =blank open curly brackets table row cell 2 x end cell cell comma text  if  end text 0 less or equal than x less or equal than fraction numerator 1 over denominator 2 end fraction end cell row cell 2 minus 2 x end cell cell comma text  if  end text fraction numerator 1 over denominator 2 end fraction less than x less or equal than 1 end cell end table close Let f((b) (x)=f(f(x)), f(n+(a) (x) = f(n)(f(x)) for each integer n 2. For how many values of x is [0, 1] is f(2008) (x) = 1/2?

    For each x in [0, 1] define f(x) =blank open curly brackets table row cell 2 x end cell cell comma text  if  end text 0 less or equal than x less or equal than fraction numerator 1 over denominator 2 end fraction end cell row cell 2 minus 2 x end cell cell comma text  if  end text fraction numerator 1 over denominator 2 end fraction less than x less or equal than 1 end cell end table close Let f((b) (x)=f(f(x)), f(n+(a) (x) = f(n)(f(x)) for each integer n 2. For how many values of x is [0, 1] is f(2008) (x) = 1/2?

    Maths-General
    General
    Maths-

    Ifblank alpha text end textandtext end text beta are the roots of the equationblank a x to the power of 2 end exponent plus b x plus c equals 0 then the quadratic equation whose roots areblank fraction numerator alpha over denominator 1 plus alpha end fraction text  and  end text fraction numerator beta over denominator 1 plus beta end fraction text  is end text

    Ifblank alpha text end textandtext end text beta are the roots of the equationblank a x to the power of 2 end exponent plus b x plus c equals 0 then the quadratic equation whose roots areblank fraction numerator alpha over denominator 1 plus alpha end fraction text  and  end text fraction numerator beta over denominator 1 plus beta end fraction text  is end text

    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.