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Question

The function f : RR defined by
fx=x-1 x-2 x-3 is
(a) one-one but not onto
(b) onto but not one-one
(c) both one and onto
(d) neither one-one nor onto

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Solution

fx=x-1x-2x-3

Injectivity:
f1=1-11-21-3=0f2=2-12-22-3=0f3=3-13-23-3=0f1=f2=f3=0
So, f is not one-one.

Surjectivity:
Let y be an element in the co domain R, such that
y=fxy=x-1x-2x-3Since yR and xR, f is onto.

So, the answer is (b).

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