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Question 11

Let f : R → R be defined as f(x) = x4. Choose the correct answer.

(A) f is one-one onto

(B) f is many-one onto

(C) f is one-one but not onto

(D) f is neither one-one nor onto.

Answer

f: R → R is defined as f(x) = x4

Let xy ∈ R such that f(x) = f(y).

does not imply that x1=x2.

For instance,

f(1) = f(-1) = 1

∴ f is not one-one.

Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2.

∴ f is not onto.

Hence, function f is neither one-one nor onto.

The correct answer is D.

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