What is the domain and range of #y= 1/(x-10)#?

1 Answer
Jul 17, 2017

Answer:

#x inRR,x!=10#
#y inRR,y!=0#

Explanation:

The denominator 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-10=0rArrx=10larrcolor(red)" excluded value"#

#rArr"domain is " x inRR,x!=10#

To find any excluded value in the range, rearrange the function making x the subject.

#rArry(x-10)=1larr" cross-multiplying"#

#rArrxy-10y=1larr" distributing"#

#rArrxy=1+10y#

#rArrx=(1+10y)/y#

#"the denominator"!=0#

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

#rArr"range is "y inRR,y!=0#