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Question

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

A
one – one but not onto
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B
onto but not one – one
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C
both one – one and onto
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D
neither one – one nor onto
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Solution

The correct option is B onto but not one – one
We have, f(x) = (x - 1)(x - 2)(x - 3)
Since, 1, 2, 3 ϵ R and f(1) = 0, f (2) = 0, f(3) = 0
f is many - one
Let y ϵ R. f(x) = y implies (x-1) (x-2) (x-3) = y
x36x2+11x6y=0 y ϵ R
Thus, onto

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