How do you find the domain and range of #y = { 1/ (x - 1) }#?

1 Answer
Oct 26, 2017

Answer:

#x inRR,x!=1,y inRR,y!=0#

Explanation:

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

#"solve "x-1=0rArrx=1larrcolor(red)" excluded value"#

#rArr"domain is "x inRR,x!=1#

#"for the range, rearrange making x the subject"#

#rArry(x-1)=1#

#rArrxy-y=1#

#rArrxy=1+y#

#rArrx=(1+y)/y#

#"the denominator "!=0#

#rArr"range is "y inRR,y!=0#
graph{1/(x-1) [-10, 10, -5, 5]}