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

2 Answers
Jul 26, 2017

Answer:

The range is #y in RR-{5/2}#

Explanation:

#f(x)=(5x-3)/(2x+1)#
Let

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

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

#2yx+y=5x-3#

#5x-2yx=y+3#

#x(5-2y)=(y+3)#

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

The domain of #x=f(y)# is #y in RR-{5/2}#

This is also #f^-1(x)=(x+3)/(5-2x)#

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

Jul 26, 2017

Answer:

#y inRR,y!=5/2#

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#