SOLUTION: given that f(x)=2x+1/3x+4 determine f^1(x)

Question 758126: given that f(x)=2x+1/3x+4 determine f^1(x)

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
given that f(x)=2x+1/3x+4 determine f^1(x)
.
I'll assume you meant:
f(x)=(2x+1)/(3x+4)
.
replace f(x) with y:
y=(2x+1)/(3x+4)
switch variables:
x = (2y+1)/(3y+4)
multiplying both sides by (3y+4):
x(3y+4) = (2y+1)
3xy+4x = 2y+1
3xy = 2y+1-4x
3xy-2y = 1-4x
y(3x-2) = 1-4x
y = (1-4x)/(3x-2)
.
So,
f^1(x) = (1-4x)/(3x-2)

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