Question # The range of the function ( f(x)=2+x-[x-3] ) is

# The range of the function ( f(x)=2+x-[x-3] ) is

(A) [5,6]

(B) [5,6)

(C) ( R )

(D) None of these

Solution

( 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)