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Question 10

# 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.

Answer

A = R - {3}, B = R - {1}

f: A → B is defined as.

.

∴ f is one-one.

Let y ∈B = R - {1}. Then, y ≠ 1.

The function f is onto if there exists x ∈A such that f(x) = y.

Now,

Thus, for any y ∈ B, there existssuch that

Hence, function f is one-one and onto.

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