# What is the domain and range of # y =1/(2x-4)#?

##### 2 Answers

The domain of

The range of

#### Explanation:

As you cannot divide by

Therefore, the domain of

To determine the range, we calculate

So,

The domain of

This is the range of

graph{1/(2x-4) [-11.25, 11.25, -5.625, 5.625]}

#### Explanation:

The denominator of y cannot be zero as this would make y

#color(blue)"undefined".# Equating the denominator to zero and solving gives the value that x cannot be.

#"solve " 2x-4=0rArrx=2larrcolor(red)" excluded value"#

#"domain " x inRR,x!=2#

#"to find excluded value/s in the range"#

#"Rearrange the function making x the subject"#

#rArry(2x-4)=1#

#rArr2xy-4y=1#

#rArr2xy=1+4y#

#rArrx=(1+4y)/(2y)#

#"the denominator cannot be zero"#

#"solve " 2y=0rArry=0larrcolor(red)" excluded value"#

#"range " y inRR,y!=0#

graph{1/(2x-4) [-10, 10, -5, 5]}