What are the 4 fundamental operation in functional notation?

Answer 1

1) You can add/subtract functions: f(x) +- g(x) = (f +- g)(x).

2) You can multiply/divide functions: f(x) */ g(x) = (f */ g)(x).

3) You can compose functions: f(x) . g(x) = (f(g(x))) = (f . g)(x).

Let f(x) = 3x + 1 and g(x) = x2

Ex 1. (f + g)(x) = x2 + 3x + 1

Ex 2. (f * g)(x) = (3x + 1) * x2 = 3x3 + x2

Ex 3. (f(g(x))) = 3(x2) + 1 (Note that you replace all the x's in the function f(x) with the whole value of g(x).