SOLUTION: What is the value of f^-1 (3/4) if f(x)= (2x-3)/(2x+4) Show work

Question 710645: What is the value of f^-1 (3/4) if
f(x)= (2x-3)/(2x+4)
Show work
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
What is the value of f^-1 (3/4) if
f(x)= (2x-3)/(2x+4)
.
Begin by finding f^(-1):
f(x)= (2x-3)/(2x+4)
y = (2x-3)/(2x+4)
flip variables and solve for y:
x = (2y-3)/(2y+4)
x(2y+4) = (2y-3)
2xy+4x = 2y-3
2xy = 2y-3-4x
2xy-2y = -3-4x
y(2x-2) = -3-4x
y = (-3-4x)/(2x-2)
y = (3+4x)/(2-2x)
f^(-1)(x) = (3+4x)/(2-2x)
.
f^-1 (3/4) = (3+4(3/4))/(2-2(3/4))
f^-1 (3/4) = (3+3)/(2-(3/2))
f^-1 (3/4) = (6)/((2/2)-(3/2))
f^-1 (3/4) = (6)/(-(1/2))
f^-1 (3/4) = -12

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