What is the domain and range of #y= -x/(x^2-1)#?

1 Answer
Jan 28, 2018

Answer:

#x inRR,x!=+-1#
#y inRR,y!=0#

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]}