What is the inverse function of #f(x) = (2x)/(x+3)#?

2 Answers
Aria
Mar 15, 2018

#f^-1(x)=(-3x)/(x-2)#

Explanation:

#f(x)=y=(2x)/(x+3)#
#xy+3y=2x#
#xy-2x=-3y#
#x(y-2)=-3y#
#x=(-3y)/(y-2)=f^-1(y)#
#f^-1(x)=(-3x)/(x-2)#

Jim G.
Mar 15, 2018

#f^-1(x)=-(3x)/(x-2)#

Explanation:

#"Rearrange making x the subject"#

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

#rArry(x+3)=2x#

#rArrxy+3y=2x#

#rArrxy-2x=-3y#

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

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

#"change y into x and we have the inverse"#

#rArrf^-1(x)=(3x)/(x-2)#

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