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Question

The correct option(s) for the function f(x)=([x]1)+(4[x]) is/are
(where [.] represents the greatest integer function).

A
Range of the function is {2,1+3}
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B
Domain of the function is [1,5)
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C
Domain of the function is (0,4]
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D
Range of the function is {3,1+2}
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Solution

The correct options are
B Domain of the function is [1,5)
D Range of the function is {3,1+2}
f(x)=([x]1)+(4[x])
For f(x) to be defined,
[x]10 and 4[x]0
1[x]4
1x<5
For,
1)x[1,2)
[x]=1
([x]1)+(4[x])=3

2)x[2,3)
[x]=2
([x]1)+(4[x])=1+2

3)x[3,4)
[x]=3
([x]1)+(4[x])=1+2

4)x[4,5)
[x]=4
([x]1)+(4[x])=3

Thus, range of the function is {3,1+2}

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