The function f : R → Rdefined 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 Bonto 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 ⇒x3−6x2+11x−6−y=0⇒ y ϵ R Thus, onto