SOLUTION: Find the inverse a) f(x) = (2x) / (1-x) b) g(x) = (2x+3) / (4x+5) c) r(x) = √(x-1) + 5 d) p(x) = (x+2)^3 -7 Can you please help me out thank you so much in advance:)

Question 917646: Find the inverse
a) f(x) = (2x) / (1-x)
b) g(x) = (2x+3) / (4x+5)
c) r(x) = √(x-1) + 5
d) p(x) = (x+2)^3 -7
Can you please help me out thank you so much in advance:)
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
a) y = 2x/(1 - x)
y - xy = 2x
y = 2x + xy
y = x(2 + y)
y/(2 + y) = x

f^(-1)(x) = x/(2 + x)

b) y = (2x + 3)/(4x + 5)
4xy + 5y = 2x + 3
4xy - 2x = 3 - 5y
x(4y - 2) = 3 - 5y
x = (3 - 5y)/(4y - 2)

g^(-1)(x) = (3 - 5x)/(4x - 2)

c) y = sqrt(x - 1) + 5
y - 5 = sqrt(x - 1)
(y - 5)^2 = x - 1
(y - 5)^2 + 1 = x

r^(-1)(x) = (x - 5)^2 + 1

d) y = (x + 2)^3 - 7
y + 7 = (x + 2)^2
sqrt(y + 7) = x + 2
sqrt(y + 7) - 2 = x

p^(-1)(x) = sqrt(x + 7) - 2
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SOLUTION: Find the inverse a) f(x) = (2x) / (1-x) b) g(x) = (2x+3) / (4x+5) c) r(x) = &#8730;(x-1) + 5 d) p(x) = (x+2)^3 -7 Can you please help me out thank you so much in advance:)

SOLUTION: Find the inverse a) f(x) = (2x) / (1-x) b) g(x) = (2x+3) / (4x+5) c) r(x) = √(x-1) + 5 d) p(x) = (x+2)^3 -7 Can you please help me out thank you so much in advance:)