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

1 Answer
Jim G.
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#

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