What is the domain and range of y= -x/(x^2-1)y=−xx2−1?
1 Answer
Jan 28, 2018
Explanation:
The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the values that x cannot be.
"solve "x^2-1=0rArr(x-1)(x+1)=0
rArrx=+-1larrcolor(red)"excluded values"
"domain is "x inRR,x!=+-1
"divide terms on numerator/denominator by "x^2
y=(x/x^2)/(x^2/x^2-1/x^2)=(1/x)/(1-1/x^2)
"as "xto+-oo,yto0/(1-0)
rArry=0larrcolor(red)"excluded value"
"range is "y inRR,y!=0
graph{-x/(x^2-1) [-10, 10, -5, 5]}
