What is the domain and range of y= 1/(x-10)?

1 Answer
Jim G.
Jul 17, 2017

x inRR,x!=10
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 "x-10=0rArrx=10larrcolor(red)" excluded value"

rArr"domain is " x inRR,x!=10

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

rArry(x-10)=1larr" cross-multiplying"

rArrxy-10y=1larr" distributing"

rArrxy=1+10y

rArrx=(1+10y)/y

"the denominator"!=0

rArry=0larrcolor(red)" excluded value"

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

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