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

1 Answer
Jul 11, 2017

x inRR,x!=0,y inRR,y!=3

Explanation:

The denominator of y cannot be zero as this would make y undefined.

rArrx=0larrcolor(red)" excluded value"

"domain is " x inRR,x!=0

To find any excluded value in the range, rearrange making x the subject.

rArrxy=3x-6larrcolor(blue)" cross-multiply"

rArrxy-3x=-6larr" collect terms in x"

rArrx(y-3)=-6larr" common factor of x"

rArrx=-6/(y-3)

"the denominator cannot equal zero"

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

"range is " y inRR,y!=3