If $f(x)=\dfrac{a}{x+2}$, solve for the value of $a$ so that $f(0)=f^{-1}(3a)$.
0 = (a-6a)/3a
-5a = 0
a = 0.
f(0) = a/2
Find the inverse
y = a / ( x + 2) get x by itself
(x + 2) y = a
x + 2 = a / y
x = a / y - 2 "swap" x and y
y = a/x - 2 = the inverse = f-1
f-1 (3a) = a / ( 3a) - 2 = (1/3) - 2 = -5/3
So
f (0) = f-1 (3a)
a/2 = -5/3
a = 2 (-5/3) = -10/3
+184 
