The range of $| x - 2 | + | x - 5 |$ is

[2, \infty)

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[3, \infty)

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[4, \infty)

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[5, \infty)

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Solution

The correct option is B $[3, \infty)$
$f (x) = | x - 2 | + | x - 5 |$ and domain of $f (x)$ is R
For $x < 2, f (x) = 2 - x + 5 - x = 7 - 2 x$ ;
For $2 < x < 5, f (x) = x - 2 + 5 - x = 3$ ;
For $x > 5, f (x) = x - 2 + x - 5 = 2 x - 7$ ;
On plotting the graph we get the Range $f = [3, \infty)$

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