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

1 Answer
Jim G.
Apr 24, 2018

#x inRR,x!=-2,y inRR,y!=1#

Explanation:

The denominator of f(x) cannot equal zero as this would make f(x) 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 "x inRR,x!=-2#

#x in (-oo,-2)uu(-2,oo)larrcolor(blue)"in interval notation"#

#"let " y=(x-2)/(x+2)#

#"For range rearrange making x the subject"#

#rArry(x+2)=x-2#

#rArrxy+2y=x-2#

#rArrxy-x=-2-2y#

#rArrx(y-1)=-2(1+y)#

#rArrx=-(2(1+y))/(y-1)#

#"solve "y-1=0rArry=1larrcolor(red)"excluded value"#

#"Range "y inRR,y!=1#

#y in(-oo,1)uu(1,oo)#
graph{(x-2)/(x+2) [-10, 10, -5, 5]}

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