How do you find the domain and range of #g(x)= 2/ (x-1)#?

1 Answer
Jim G.
May 1, 2017

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

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

Explanation:

The denominator of g(x) cannot be zero as this would make g(x) #color(blue)"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 " x inRR,x!=1#

#"To find the excluded value/s in the range"#

#"Rearrange g(x) and make x the subject"#

#g(x)=y=2/(x-1)larrcolor(blue)" cross-multiply"#

#y(x-1)=2#

#xy-y=2#

#xy=2+y#

#rArrx=(2+y)/y#

#" the denominator cannot be zero"#

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

#rArr"range " y inRR,y!=0#
graph{2/(x-1) [-10, 10, -5, 5]}

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