# What is the range of the function #f(x)=(5x-3)/(2x+1)#?

##### 2 Answers

Jul 26, 2017

The range is

#### Explanation:

Let

The domain of

This is also

graph{(5x-3)/(2x+1) [-22.8, 22.83, -11.4, 11.4]}

Jul 26, 2017

#### Explanation:

#"given "y=(5x-3)/(2x+1)#

#"rearrange making x the subject"#

#rArry(2x+1)=5x-3larrcolor(blue)"cross-multiplying"#

#rArr2xy+y=5x-3larrcolor(blue)" distributing"#

#rArr2xy-5x=-3-ylarrcolor(blue)" collect terms in x"#

#rArrx(2y-5)=-(3+y)larrcolor(blue)" factor out x"#

#rArrx=-(3+y)/(2y-5)#

#"the denominator cannot equal zero as this would"#

#"be undefined"#

#2y-5=0rArry=5/2larrcolor(red)" excluded value"#

#"range is "y inRR,y!=5/2#