If f(x)=square root (6x+12) then f^-1=1/square root(6x+12)?

f(x) = (6x+12)^(1/2).

To find
the inverse function of f(x).

Let f^(-1) (x) = y be the
inverse function of f(x).

 The x =
f(y).

By definition, f(y) =  put y in  place of x iin
(6x+12)^1/2).

=> f(y) =
(6y+12)^(1/2).

=> x =
(6y+12)^(1/2).

We square both
sides:

x^2 = 6y+12.

x^2-12 =
6y.

Therefore y =
1/6(x^2-12).

Therefore f^(-1) (x) =  y = (1/6)x^2 - 2 is
the inverse of f(x).  f^(1) (x) = y i= not 1/sqrt(6x+12).