Question

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 1

f: R → R is defined as

Let x, y ∈ R such that f(x) = f(y).

∴does not imply that.

For instance,

∴ 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.