To determine if two functions are inverses, we have to compose the functions into each other and get a value of x.
f(g(x)) = [tex]3(\sqrt{\frac{x - 12}{3} })^{2} - 12[/tex]
The square root and the square cancel each other out.
f(g(x)) = [tex]3(\frac{x - 12}{3}) - 12[/tex]
The 3's cancel each other out.
f(g(x)) = x - 12 - 12 = x - 24
since f(g(x)) = x - 24, these two functions are not inverses of each other.
