f(x)=2-9x find f^-1(6)

To find f^(-1)(6), you need to find the inverse function of f(x) = 2 - 9x and then substitute 6 into the inverse function.

First, let's find the inverse function of f(x):
1. Replace f(x) with y: y = 2 - 9x.
2. Swap the variables x and y: x = 2 - 9y.
3. Solve the equation for y:
Subtract 2 from both sides: x - 2 = -9y.
Divide both sides by -9: (x - 2)/(-9) = y.
4. Replace y with f^(-1)(x):
f^(-1)(x) = (x - 2)/(-9).

Now, substitute 6 into the inverse function, f^(-1)(x):
f^(-1)(6) = (6 - 2)/(-9).
Simplify the expression:
f^(-1)(6) = 4/(-9).

Therefore, f^(-1)(6) = -4/9.