Composite Functions & Operations

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

To find (f∘g)(x), first evaluate g(x) and then substitute that result into f(x).

The product of two functions is given by (f*g)(x) = f(x) * g(x).

(f∘g)(x) means applying g first and then f, while (g∘f)(x) means applying f first and then g. They are generally not equal.

(f∘g)(0) = f(g(0)) = f(-2) = 4.

(f*g)(x) = 3x³ - 14x² + 9x - 4.

g(f(x)) = 18x² - 84x + 90.

The quotient of two functions is given by (f/g)(x) = f(x) / g(x), provided g(x) ≠ 0.

(g/f)(x) = (x - 2)/(x + 3).

The order of operations is crucial because it determines which function is applied first, affecting the final result.