Which is derived because luckily when you plug 0 into f(x) :
f(0) = 4, meaning that f^-1(4) = 0 , which means that f^-1(a) = 0.
From there you can use the Theorem (f^-1) (a) = 1 / f (f^-1(a))
f^-1(a) = 0
(f^-1) (a) = 1 / f (0)
f = 6x^2 + 6x + 7
f (0) = 7
(f^-1) (a) = 1/7