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If f: AvecBa n dg: BvecC are one-one ...

If `f: AvecBa n dg: BvecC` are one-one functions, show that `gof` is one-one function.

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Algorithm of one-one function

Statement I: f : A->B is one - one and g : B->C is a one - one function, then gof :A->C is one - one Statement II : If f:A->B, g:B->A are two functions such that gof=IA and fog=IB, then f=g-1. Statement III : f(x)=sec 2x-tan2x,g(x)=cosec2x-cot2x, then f=g

Knowledge Check

  • Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

    A
    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
    B
    Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.
    C
    Statement -1 is True, Statement -2 is False
    D
    Statement -1 is False, Statement -2 is True

  • Which of the following is one-one function ?

    A
    `e^(x)`
    B
    `e^(x^(2))`
    C
    `sinx`
    D
    None of these

  • Which of the functions defined below is one one function ?

    A
    `f(x) = ((x^(3)+1)/(x^(4)+x^(2)+1)), (x in R)`
    B
    `g(x) = x + (1)/(x), (x in R^(+))`
    C
    `h(x) = x^(2) + 4x - 5(x in R)`
    D
    `f(x) = e^(-x), (x in R, x le 0)`

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    Let A be a finite set.If f:A rarr A is a one-one function,show that f is onto also.

    Let A be a finite set.If f:A rarr A is an onto function,show that f is one-one also.

    If f(x)=(x^(2)-x)/(x^(2)+2x), show that f is one-one function.

    Let A be a finite set.If f:A rarr A is an onto function,show that f is one-one also.

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