What is the domain and range of #y=1/(3x-2)#?

1 Answer
Jim G.
Apr 8, 2017

#x inRR,x!=2/3#
#y inRR,y!=0#

Explanation:

The denominator of y cannot be zero as this would make y #color(blue)"undefined".#Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "3x-2=0rArrx=2/3larrcolor(red)" excluded value"#

#rArr"domain is " x inRR,x!=2/3#

#"Rearrange to make x the subject"#

#y(3x-2)=1#

#rArr3xy-2y=1#

#rArr3xy=1+2y#

#rArrx=(1+2y)/(3y)#

#"solve " 3y=0rArry=0larrcolor(red)" excluded value"#

#rArr"range is " y inRR,y!=0#
graph{1/(3x-2) [-10, 10, -5, 5]}

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