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

2 Answers
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)

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)