Suppose f(x) = 3/(2 + x). If g(x)=f^{-1}(x)+9$, find g(3).
f ( x) = 3/ (2 + x)
Write
y = 3 / (2 + x) get x by itself
y ( 2 + x) = 3
2y + xy = 3
xy = 3 - 2y
x = (3 - 2y) / y "swap" x and t
y = (3 - 2x) / x this is the inverse = f-1(x)
So
g(3) = (3 - 2*3) / 3 + 9 = -3/3 + 9 = 8
