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

##### 1 Answer

May 1, 2017

#### 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]}