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Question

Range of the function f(x)=|x1|+|x2|+|x+1|+|x+2| where xϵ[2,2], is


A

[6,8]

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B

[2,4]

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C

[0,4]

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D

{1,2}

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Solution

The correct option is A

[6,8]


f(x)=|x1|+|x2|+|x+1|+|x+2|
When xϵ[2,1]f(x)=(x1)(x2)(x+1)+x+2=2x+4
When xϵ[1,1], f(x)=(x1)(x2)+x+1+x+2=6
When xϵ[1,2], f(x)=(x1)(x2)+x+1+x+2=2x+4
Plotting the graph of the function, range of f(x)=[6,8]


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