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

2 Answers
Narad T.
Jul 26, 2017

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]}

Jim G.
Jul 26, 2017

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

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