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Let RR be the set of all real numbers an...

Let `RR` be the set of all real numbers and `A={x in RR : 0 lt x lt 1}`. Is the mapping `f : A to RR`defined by f(x)`=(2x-1)/(1-|2x-1|)` bijective ?

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Yes
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Let RR be the set of real numbers and A={x in RR :-1 lt x lt 1}=B . Is the mapping f: A to B defined by f(x) =(x)/(1+|x|) bijective ? Justify your answer.

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Knowledge Check

  • Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

    A
    `{4,-4}`
    B
    `{1,-1}`
    C
    `{2,-2}`
    D
    `{3,-3}`

  • Let RR be the set of real numbers and the functions f: RR to RR and g : RR to RR be defined by f(x ) = x^(2)+2x-3 and g(x ) = x+1 , then the value of x for which f(g(x)) = g(f(x)) is -

    A
    `-1`
    B
    `0`
    C
    `1`
    D
    `2`

  • Let RR be the set of real numbers and f : RR to RR be defined by f(x)=sin x, then the range of f(x) is-

    A
    `{f (x) in RR : 0 le f (x) le 1}`
    B
    `{f (x) in RR: -1 lt f (x) lt 1}`
    C
    `{f (x) in RR : -1 lt f(x) le 1}`
    D
    `{ f (x) in RR : -1 le f(x) le 1}`

    • Similar Questions

    Explore conceptually related problems

    Let RR be the set of all real numbers and for all x in RR , the mapping f: R to R is dedined by f(x) = ax +2. if ( fo f ) =T_(RR) , then find the value of a.

    Let A={x in RR:-1 le x le 1} =B . Prove that , the mapping from A to B defined by f(x)= sin pi x is surjective.

    Let RR be the set of real number and f: RR rarr RR , be given by f(x)=2x^(2)-1 . .Is this mapping one -one ?

    Let RR be the set of real numbers and A=R-{3},B=R-{1} . Show that , f: A rarr B defined by , f(x) =(x-1)/(x-3) is a one-one onto function.

    Let A=RR-{2} and B=RR-{1} . Show that, the function f:A rarr B defined by f(x)=(x-3)/(x-2) is bijective .

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