Question

The question(s) are as follows:
Given: f(x) = 3cos(3x+π) - 4
Find:
a) the inverse of F(x)
b) the domain and range of F(x)
c) the domain and range of F -1(x)

I got cos-1[(x-4)/9] - π = y for the inverse, although I'm not sure I did the problem right (I set x to y and y to x and then solved for y).
For the domain of F-1(x) I got [-5,5] and for the range I got [-π/3,1- π/3]
Is this right?

For cos(3x+π) = 4/3, don't I have to finish solving cos(3x+π) before I decide that there is no solution (Since 4/3 isn't between -1 and 1)? I have been doing these and other problems for so long today that I am getting more confused - not less, lol! Thanks for your help.