Given f(x) = x-3 and g(x) = 4-5x, find the compositions and identify the domain for each new function using interval notation.

(a) (fg)(x)

(b)(gf)(x)

(c) (gg)(x)

For each function below , identify the parent functions and list the transformations that would be used. Possible parent functions: y=x , y = x^2 , and y = |x|.

(a) f(x) = 1/2 (x+3)^2 +5

(b) g(x) = - |x-4| - 2

(c) h(x) = 4x+2 -1