Question

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 1

The given function f:R→R is defined by f(x)= x 4 .

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

⇒ x 4 = y 4 ⇒x=±y

It can be observed that f( x )=f( y ) does not implies x=y. So, f is not one-one.

Let, −5 be an element in co-domain R. There does not exist any element x in the domain R such that, f( x )=−5.

So, f is not onto.

The function f:R→R , defined by f( x )= x 4 is neither one-one nor onto.

Hence, option (D) is correct.