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Let f: R to R be defined as f(x) = x-1 ...

Let `f: R to R ` be defined as `f(x) = x-1 and g : R -{1,-1} to R ` be defined as `g(x) = (x^(2))/(x^(2)-1)`
Then the function fog is :

A

One - one but not onto

B

onto but not one - one

C

both one - one and onto

D

neither one - one nor onto

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Knowledge Check

  • Let f :R to R be fefined as f(x) = 2x -1 and g : R - {1} to R be defined as g(x) = (x-1/2)/(x-1) Then the composition function ƒ(g(x)) is :

    A
    onto but not one-one
    B
    both one-one and onto
    C
    one-one but not onto
    D
    neither one-one nor onto

  • If f:R to R be defined by f(x)=3x^(2)-5 and g: R to R by g(x)= (x)/(x^(2)+1). Then, gof is

    A
    `(3x^(2)-5)/(9x^(4)-30x^(2)+26)`
    B
    `(3x^(2)-5)/(9x^(4)-6x^(2)+26)`
    C
    `(3x^(2))/(x^(4)+2x^(2)-4)`
    D
    `(3x^(2))/(9x^(4)+30x^(2)-2)`

  • The function f:R rarr R defined as f(x)=(x^(2)-x+1)/(x^(2)+x+1) is

    A
    injective as well as sujective
    B
    injective but not surjective
    C
    surjective but not injective
    D
    neither injective nor surjective
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