What is the domain and range of #y=5/(x-1)#?

1 Answer
Mar 5, 2018

Answer:

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

Explanation:

#"the denominator of y cannot equal 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#

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

#rArry(x-1)=5#

#rArrxy-y=5#

#rArrxy=5+y#

#rArrx=(5+y)/y#

#rArry=0larrcolor(red)"excluded value"#

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