The range of the function ( f(x)=2+x-[x-3] ) is
(A) [5,6]
(B) [5,6)
(C) ( R )
(D) None of these

( operatorname{dos} quad 0 leq x<1 )
[
begin{array}{l}
begin{aligned}
-3 leq &(x-3) leq-2
therefore quad[x-3] &=-3
therefore quad f(x) &=2+x+3=5+x
end{aligned}
end{array}
]
and since ( 0 leq x<1 )
[
f(x) in[5f]
]
bon
[
begin{array}{l}
quad begin{array}{l}
1 leqslant x<2
-2 leq(x-3)<-1
therefore quad[x-3]=-2
f(x)=2+x-(-2)=4+x
end{array}
end{array}
]
and since ( x inleft[begin{array}{ll}1 & 2end{array}right) )
[
f(x) in[5 quad 6)
]
Similaily the same for all ( x ) intarals
( therefore ) Dange of ( b(x)  ) is [56)