How do you find the domain and range for #y=2/(5(x-2))#?

1 Answer
Aug 28, 2017

Answer:

#x inRR,x!=2#
#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 "5(x-2)=0rArrx=2larrcolor(red)" excluded value"#

#rArr"domain is "x inRR,x!=2#

#"to find any excluded values in the range rearrange making"#
#"x the subject"#

#rArry(5x-10)=2larrcolor(blue)" cross-multipling"#

#rArr5xy-10y=2#

#rArr5xy=2+10y#

#rArrx=(2+10y)/(5y)#

#"the denominator cannot equal zero"#

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

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