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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

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Solution

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

Assume x,yR 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:RR , defined by f( x )= x 4 is neither one-one nor onto.

Hence, option (D) is correct.


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