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

##### 2 Answers

The domain is

#### Explanation:

The function is

As the denominator must be

Therefore,

The domain is

To calculate the range, proceed as follows :

Cross multiply

As the denominator must be

The range is

graph{1/(x+1) [-16.02, 16.02, -8.01, 8.01]}

#### Explanation:

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

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

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

#"to find range, rearrange making x the subject"#

#y(x+1)=1#

#xy+y=1#

#xy=1-y#

#x=(1-y)/y#

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

#"range is "y in(-oo,0)uu(0,oo)#

graph{1/(x+1) [-10, 10, -5, 5]}