Given #f(x) = (2x)/(x+3)#, how do you find #f^(-1) (4)#?

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Given #f(x) = (2x)/(x+3)#, how do you find #f^(-1) (4)#?

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Answer 1 · 2015-08-07T14:54:11

I found: #f^-1(4)=-6#

Explanation:

I start rearranging the original function #y=f(x)=(2x)/(x+3)# solving it for #x# to get:
#(x+3)*y=2x#
#xy+3y-2x=0#
#xy-2x=-3y#
#x(y-2)=-3y#
and:
#x=f(y)=(-3y)/(y-2)# or changing #x# with #y# you get:
#f^-1(x)=(-3x)/(x-2)#
and
#f^-1(4)=(-3*4)/(4-2)=-12/2=-6#

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Given #f(x) = (2x)/(x+3)#, how do you find #f^(-1) (4)#?

1 Answer

Explanation:

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