The function f,defined by f(x)=x-1/3-x, has the same set as domain and as range. This statement is true/false?Please give reasons for your answer.

1 Answer
Feb 10, 2018

#"false "#

Explanation:

#f(x)=(x-1)/(3-x)#

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "3-x=0rArrx=3larrcolor(red)"is excluded value"#

#rArr"domain is "x inRR,x!=3#

#"to find the range rearrange making x the subject"#

#y=(x-1)/(3-x)#

#rArry(3-x)=x-1#

#rArr3y-xy-x=-1#

#rArr-xy-x=-1-3y#

#rArrx(-y-1)=-1-3y#

#rArrx=(-1-3y)/(-y-1)#

#"the denominator "!=0#

#rArry=-1larrcolor(red)"is excluded value"#

#rArr"range is "y inRR,y!=-1#

#"the domain and range are not the same"#
graph{(x-1)/(3-x) [-10, 10, -5, 5]}