Define the sum of any two functions with the same domain to be the function f + g such that for each x in the
domain of f and g, (f + g)(x) = f(x) + g(x). define the product of any two functions to be the function ff, such
that for each x in the domain of f and g, (ff)(x) = ((
let f, g, and ℎ be real-valued functions defined by the equations f(x) = 3x + 1, g(x) = −12
x + 2, and
ℎ(x) = x2 − 4.
a. does f(g + ℎ) = ff+ fℎ?
b. show that this is true for any three functions with the same domains.
c. does f ∘ (g + ℎ) = f ∘ g + f ∘ ℎ for the functions described above?