If $f (x) = | x - 1 | + | x - 2 | + | x - 3 |$ when $2 < x < 3$ is

one one function only

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an onto function only

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an into function

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an identity function

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Solution

The correct option is D an identity function
$f (x) =∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣$
$= (x - 1) + (x - 2) - (x - 3)$ when $2 < x < 3$
$= x$
$∴ f (x)$ is an identity function

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