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Which of the following defines as one - ...

Which of the following defines as one - one function ?

A

`f(x)=e^(x)(-oo lt x lt oo)`

B

`f(x)=e^(x^(2))(-oo, lt xlt oo)`

C

`f(x)=cosx(0le x le pi)`

D

`f(x)=ax+b (-oo, lt x lt oo)(a ne 0)`

Text Solution

Verified by Experts

The correct Answer is:
A,B,D
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Knowledge Check

  • Which of the following functions is one-one?

    A
    `fR to R " is given by"f(x)=2x^(1)+1"For all " x in R`
    B
    `g:Z to Z " given by"g(x)=x^(4)"For all " x in Z`
    C
    `h:R to R " given h"(x)=x^(3)+4"For all " x in R`
    D
    `phi:C to C " given by "phi(z)=z^(3)+4"For all " z in C`

  • Which of the following is one-one function ?

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

  • Which one of the following functions is one-one?

    A
    `f:R to R" given by "f(x)|x-1|"for all "x in R`
    B
    `g:[-pi//2,pi//2] in R` is given by:
    `g(x)=|sin x|"for all "x in[-pi//2,pi//2]`
    C
    `h:[-pi//2,pi//2] in R` is given by
    `h=(x)=sin x" for all "x in [-pi//2, pi//2]`
    D
    `phi: R to R "given by" f(x)=x^(2)-4"for all x " inR`

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    State which of the following functions are one-one and why? f:R.{1}toR defined by f(x)=(x+1)/(x-1)

    Which one of the following is a function

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    Which of the functions defined below is one one function ?

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