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Verify whether the function f : A to B ,...

Verify whether the function `f : A to B` , where A = R - {3} and B = R -{1}, defined by `f(x) = (x -2)/(x -3)` is one-one and onto or not. Give reason.

Text Solution

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The correct Answer is:
f is both one-one and onto.
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Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

Let A = R - {3} and B =R -{1}. Consider the function f : A to B defined by f (x) = ((x -2)/(x -3)). Is f one-one and onto ? Justify your answer.

Knowledge Check

  • Function f: R rarr R , defined by f(x)=x^(2)+x is

    A
    one-one, onto
    B
    one-one, into
    C
    many one, onto
    D
    many one, into

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