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If f: R to R and g: R to R are given by ...

If `f: R to R` and `g: R to R` are given by `f(x)= cosx` and `g(x) =3x^(2)`.Show that `gof ne fog`

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If f: R to R and g : R to R are given by by f(x)=cos x and g(x)=3x^(2) , then shown that gof ne fog .

If f:RtoRandg:RtoR are given by f(x)=cosxandg(x)=3x^(2) . Find gof and fog.

Knowledge Check

  • If f:R rarr R and g : R rarr R are defined by f(x) = 3x + 2 and g(x) = x^2 - 3 , then the value of x such that g(f(x))=4 are

    A
    a.`-1/3, 1`
    B
    b.`-1/3, -1`
    C
    c.1/3, -1
    D
    d.1/3, 1

  • If f: (R) rarr (R) and g (R) rarr (R) defined by f(x)=2x+3 and g(x)=x^(2)+7 ,then the values of x such that g(f(x))=8 are

    A
    1)1,2
    B
    2)-3
    C
    3)-3
    D
    4)-1,-2

  • f: R to R and g: [0,oo)to R is defined by f(x) = x^(2) and g(x) = sqrtx . Which one of the following is not true?

    A
    gof (4) = 4
    B
    fog (2) = 2
    C
    fog (- 4) = 4
    D
    gof (- 2) = 2

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    Explore conceptually related problems

    Find fog if f(x)= x-2 and g(x) = 3x

    Find gof and fog if f : R rarr R and g : R rarr R are given by f(x) = cosx and g(x) = 3x^(2)

    If functions f : R to R and g: R to R are given by f(x) = |x| and g(x) = [x] , ( where [x] is greatest function) find fog (-(1)/(2) ) and "gof" (- (1)/(2) )

    If functions f: R -gt R and g : R -gt R arc given by f(x) = abs(x) and g(x) =abs(x) , (where abs(A) is indicatescates: integer function) find f o g(abs(-1/2)) and go f(-1/2) .

    If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) (sqrt(pi))/(2) "and (gof)"((pi)/(3)) .

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