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

1 Answer
May 25, 2018

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

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"solve x+1=0x=1excluded value

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

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

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

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

xy+y=-1xy+y=1

xy=-1-yxy=1y

x=-(1+y)/yx=1+yy

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

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