Question 11
Let f : R → R be defined as f(x) = x^{4}. 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) = x^{4}

Let *x*, *y* ∈ **R** such that *f*(*x*) = *f*(*y*).

∴does not imply that x_{1}=x_{2}.

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.