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in Sets, relations and functions by (53.1k points)

The function f R: → R defined by f (x) = (x - 1)(x - 2)(x - 3) is

(A)  One-to-one but not onto

(B)  Onto but not one-to-one

(C)  Both one-to-one and onto

(D)  Neither one-to-one nor onto

1 Answer

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by (53.3k points)
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Best answer

Correct option (B, D)

Explanation :

We have

f(x) = (x - 1)(x - 2)(x - 3) and 

f(1) = f(2) = f(3) = 0

which implies that f x( ) is not one-to-one. For each y ∈ R  , there exists x ∈ R  such that f (x) = y. Therefore, f is onto. Hence, f R: → R is onto but not one-to-one. 

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