+501 Suppose $f(x)=\frac{3}{2-x}$. If $g(x)=\frac{1}{f^{-1}(x)}+9$, find $g(3)$.
+129852 Let's find the inverse.....write
y = 1 / (3 -x) get x by itself
(3-x) y = 1
3y - xy = 1
3y - 1 = xy
(3y - 1) / y = x "swap" x and y
(3x - 1) / x = y = the inverse
So
g(x) = 1/ inverse + 9 =
1 / (3x - 1) / x + 9 =
x /( 3x - 1) + 9
So
g(3) = 3 / ( 3*3 - 1) + 9 = (3/8) + 9 = [ 75] / 9 = 25 / 3
