M647 Function Operations

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as (f ∘ g)(x) = f(g(x)).

The formula for finding (f + g)(x) is (f + g)(x) = f(x) + g(x).

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

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

(g ∘ h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

A function is a relation that assigns exactly one output for each input from a set of inputs, called the domain.

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

The range of a function is the set of all possible output values (dependent variable) that result from using the function.

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, typically in the form f(x) = mx + b.

In a quadratic function of the form f(x) = ax^2 + bx + c, 'a' determines the direction of the parabola, 'b' affects the position of the vertex, and 'c' is the y-intercept.