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Let a function f:(0,infty)to[0,infty) be...

Let a function `f:(0,infty)to[0,infty)` be defined by `f(x)=abs(1-1/x)`. Then f is

A

injective but not surjective

B

both injective as well as surjective

C

not injective but it is surjective

D

neiher injective nor surjective

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let f: (1 to infty) to (1, infty) be defined by f(x) =(x+2)/(x-1) . Then

    A
    f is 1 - 1 and onto
    B
    f is 1 - 1 but not onto
    C
    f is not 1 - 1 but onto
    D
    f is neither 1 - 1 nor onto

  • Leet f : [0,infty) rarr [0,2] be defined by f(x) = (2x)/(1+x) then f 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

  • If the function f : [1, infty) rarr[1, infty) is defined by f(x) = 2^(x(x-1)) is invertible, then f^(-1)(x) is

    A
    `(1/2)^(x(x-1))`
    B
    `1/2(1+sqrt(1+ 4 log_2x))`
    C
    `1/2(1-sqrt(1+ 4 log_2x))`
    D
    not defined

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