If $f (x^{3} - 6 x^{2} + 11 x - 3) = x - 1,$ then $f (3) =$

0

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1

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2

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3

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Solution

The correct option is C $2$
$f (x^{3} - 6 x^{2} + 11 x - 3) = x - 1$
$x^{3} - 6 x^{2} + 11 x - 3 = 3 \Rightarrow (x - 1) (x^{2} - 5 x + 6) = 0 \Rightarrow (x - 1) (x - 2) (x - 3) = 0$
$\Rightarrow x = 1, 2, 3$
So,
$x = 1 \Rightarrow f (3) = 1 - 1 = 0$
$x = 2 \Rightarrow f (3) = 2 - 1 = 1$
$x = 3 \Rightarrow f (3) = 3 - 1 = 2$

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