If f(x) = a/(x + 2), solve for the value of a so that f(0)=f^{-1}(8a).
f(0) = a/2
And we can find f-1 as follows
y = a /(x + 2) get x by itself
y ( x + 2) = a
yx + 2y = a
yx = a - 2y
x = (a - 2y) / y swap x, y
y = (a - 2x) / x = f-1 (x)
f-1(8a) = (a - 2(8a)) / (8a) = -15a / (8a) = -15/8
So
a/2 = -15/8
a = -15/4
