What is the domain and range of y=1/(3x-2)y=13x−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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