The range of -x-2-x-5- isA- -2- -B- -3- -C- -4- -D- -5- -

The correct option is B [3,∞ )f(x)=|x 2|+|x 5| and domain of f(x) is R For x lt;2, f(x)=2 x+5 x=7 2x; For 2 lt;x lt;5, f(x)=x 2+5 x=3; For x gt;5 ,f(x) ...

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Standard XII

Mathematics

Using Graph to Find Range of a Function

The range of ...

Question

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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The range of |x−2|+|x−5| is

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

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

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 $f = [3, \infty)$