What is the domain and range of f(x) = (x-2) / (x+2)?
1 Answer
Apr 24, 2018
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]}
