# What is the domain and range of #f(x)=(2x-1)/(3-x)#?

##### 2 Answers

#### 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 "3-x=0rArrx=3larrcolor(red)" excluded value"#

#"domain is "x inRR,x!=3# To find any excluded values in the range rearrange f(x) making x the subject.

#y=(2x-1)/(3-x)#

#rArry(3-x)=2x-1larrcolor(blue)" cross-multiplying"#

#rArr3y-xy=2x-1#

#rArr-xy-2x=-3y-1larrcolor(blue)" collecting terms in x together"#

#rArrx(-y-2)=-(3y+1)#

#rArrx=-(3y+1)/(-y-2)#

#"the denominator cannot equal zero"#

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

#rArr"range is "y inRR,y!=-2#

The domain is

#### Explanation:

The function is

The denominator must be

So,

The domain is

Let,

The range is

graph{(y-(2x-1)/(3-x))=0 [-58.53, 58.54, -29.26, 29.24]}