What is the domain and range of 1/(x+2)?

1 Answer
Jim G.
Nov 24, 2017

x inRR,x!=-2
y inRR,y!=0

Explanation:

"let "y=1/(x+2)

"the denominator of y cannot be zero as this would"
"make y undefined. Equating the denominator to zero"
"and solving gives the value that x cannot be"

"solve "x+2=0rArrx=-2larrcolor(red)"excluded value"

rArr"domain is "x inRR,x!=-2

"to find the range rearrange making x the subject"

rArry(x+2)=1

rArrxy+2y=1

rArrxy=1-2y

rArrx=(1-2y)/y

"the denominator cannot be zero"

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

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