# What is the domain and range of #y=(4+x)/(1-4x)#?

##### 2 Answers

The domain is

The range is

#### Explanation:

As you cannot divide by

So,

The domain is

To find the range, we calculate the inverse function

We interchange

We express

The inverse is

The range of

The range is

#### Explanation:

#"the domain is defined for all real values of x, except"#

#"those values which make the denominator zero"#

#"to find excluded values equate the denominator to zero"#

#"and solve for x"#

#"solve " 1-4x=0rArrx=1/4larrcolor(red)"excluded value"#

#rArr"domain is " x inRR,x!=1/4#

#"to find any excluded values in the range, change the subject"#

#"of the function to x"#

#y(1-4x)=4+x#

#rArry-4xy=4+x#

#rArr-4xy-x=4-y#

#rArrx(-4y-1)=4-y#

#rArrx=(4-y)/(-4y-1)#

#"the denominator cannot equal zero"#

#rArr-4y-1=0rArry=-1/4larrcolor(red)" excluded value"#

#rArr"range is " y inRR,y!=-1/4#