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

f: R → R be defined as f(x) = x⁴.

Let x, y ϵ R such that f(x) = f(y)

⇒ x⁴ = y⁴

⇒ x = �y

Therefore, f(x₁) = f(x₂) which does not implies x₁ = x₂.

For instance, f(1) = f(-1) = 1

Therefore, f is not one-one.

Now, an element 2 in co-domain R.

We can see that there does not exist any x in domain R such that

f(x) = 2

Therefore, f is not onto.

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