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

1 Answer
Nov 24, 2017

Answer:

#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#