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 g(f(x)), substitute f(x) into g(x).

The formula for adding two functions f and g is (f + g)(x) = f(x) + g(x).

The formula for subtracting two functions f and g is (f - g)(x) = f(x) - g(x).

The formula for multiplying two functions f and g is (f * g)(x) = f(x) * g(x).

The formula for dividing two functions f and g is (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

To simplify a function at a specific value, substitute the value into the function and perform the arithmetic operations.

f(g(x)) = 2(x^2 + 3) = 2x^2 + 6.

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

(f∘g)(0) = f(g(0)) = f(-2) = 3(-2) + 10 = 4.