AA2 Operations with Function/ Composite Functions

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

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

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

Given j(x) = ∛(x-1) and h(x) = x^3 + 1, find j(h(x)).

Back

j(h(x)) = x.

Front

What is the difference of two functions g(x) and h(x)?

Back

The difference of two functions g(x) and h(x) is defined as (g - h)(x) = g(x) - h(x).

Front

Given g(x) = -x^2 + 4x and h(x) = x + 3, find (g - h)(x).

Back

(g - h)(x) = -x^2 + 3x - 3.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point a, substitute x with a in the function: f(a).

Front

Evaluate f(-5) if f(x) = 3x^2 + 7x.

Back

f(-5) = 0.

Front

What is the notation for function composition?

Back

Function composition is denoted by (f ∘ g)(x) or f(g(x)).

Front

Given f(x) = 3x - 2 and g(x) = 4x, find f(g(x)).

Back

f(g(x)) = 3(4x) - 2 = 12x - 2.