find the inverse...?

Question

f(x)=(3+exp(x))/(3-exp(x))

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Answer 1

f(x)=(3+exp(x))/(3-exp(x))
substituting y for f(x),
y = (3 + e^x)/(3 - e^x)
The inverse will be
x = (3 + e^y)/(3 - e^y)
x(3 - e^y) = (3 + e^y)
3x - xe^y = 3 + e^y
e^y + xe^y = 3x - 3
e^y(x + 1) = 3x - 3
e^y = (3x - 3)/(x + 1)
y = ln[(3x - 3)/(x + 1)]
f^-1(x) = ln[(3x - 3)/(x + 1)]

Answer 2

f(x) = [3+exp(x)]/[3-exp(x)]
[3+exp(x)]/[3-exp(x)] = y
3+exp(x) = y[3-exp(x)]
3+exp(x) = 3y -y[exp(x)]
3-3y = -y[exp(x)]-exp(x)
-{y[exp(x)]+exp(x)} = 3-3y
y[exp(x)]+exp(x) = 3y-3
exp(x)[y+1] = 3y-3
exp(x) = (3y-3)/(y+1)
x = ln[(3y-3)/(y+1)
x = ln(3y-3) - ln(y+1)
inverse of f(x) = ln(3x-3) - ln(x+1)

Answer 3

ha ha ha ha ha.... good luck with that.