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f:R to R is defined by f(x)==(e^(x^(2))-...

`f:R to R` is defined by f(x)=`=(e^(x^(2))-e^(-x^(2)))/(e^(x^(2))+e^(-x^(2)))`, is

A

one-one but not onto

B

many-one but onto

C

one-one and onto

D

neither one-one nor onto

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Let f:R rarr R" be defined by "f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)). Then

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

  • Let f:R rarr R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^(x)+e^(-x)) then :

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

  • The inverse of the function f:R to {x in R: x lt 1}"given by "f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x)), is

    A
    `(1)/(2)"log" (1+x)/(1-x)`
    B
    `(1)/(2)"log" (2+x)/(2-x)`
    C
    `(1)/(2)"log" (1-x)/(1+x)`
    D
    None of these

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