What is the domain and range for #f(x) = - ( 1 / ( x + 1) )#?

1 Answer
May 25, 2018

Answer:

#x in(-oo,-1)uu(-1,oo)#
#y in(-oo,0)uu(0,oo)#

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "x+1=0rArrx=-1larrcolor(red)"excluded value"#

#"domain "x in(-oo,-1)uu(-1,oo)#

#"for the range rearrange making x the subject"#

#y=-1/(x+1)#

#y(x+1)=-1#

#xy+y=-1#

#xy=-1-y#

#x=-(1+y)/y#

#y=0larrcolor(red)"excluded value"#

#"range "y in(-oo,0)uu(0,oo)#
graph{-1/(x+1) [-10, 10, -5, 5]}