Let A = R – {3} and B = R – {1}. Consider the function f: A → B defined by
. Is f one-one and onto? Justify your answer.
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Given function:
Checking for one-one function:
Putting
Hence, if
Thus, the function f is one-one function.
Checking for onto function:
Let f(x) = y such that y B i.e. y ∈ R
For y = 1, x is not defined But it is given that. y ∈ R
Hence, x = (3y- 2)/(y- 1) ∈ R -{3} Hence, f is onto
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