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Question

Let f(x)=|x1|+|x2|. Then which of the following is/are true?

A
If xR, then f(x)[0,)
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B
If 1x3, then f(x)[1,5]
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C
f(x)=1 for all x[1110,1910]
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D
f(2)+f(32)=f(5)
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Solution

The correct options are
B If 1x3, then f(x)[1,5]
C f(x)=1 for all x[1110,1910]
f(x)=|x1|+|x2|
f(x)=32x, if x<1 1, if 1x22x3, if x>2


Domain : xR
Range : f(x)[1,)

If 1x3, then
f(1)=5,f(3)=3
f(x) is decreasing from 5 to 1 and then increasing to 3.
f(x)[1,5]

f(x)=1 x[1,2]

f(2)+f(32)=7+1=8
and f(5)=7
f(2)+f(32)f(5)

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