Interpreting Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as (f ∘ g)(x).

Front

What is the correct setup for (g ∘ f)(x) given f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

The correct setup is g(f(x)) = 8 - 7(3x - 2).

Front

What do you type into DESMOS for (f ∘ g)(7) if f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

You type f(g(7)).

Front

What is the difference between (f + g)(x) and (f ∘ g)(x)?

Back

(f + g)(x) is the sum of the functions evaluated at x, while (f ∘ g)(x) is the composition of f and g, meaning you first apply g to x and then apply f to the result.

Front

What is the correct setup for (f - g)(x) given f(x) = 3x - 2 and g(x) = 8 - 7x?

Back

The correct setup is (f - g)(x) = (3x - 2) - (8 - 7x).

Front

How do you evaluate (f ∘ g ∘ h)(7) using functions f, g, and h?

Back

You evaluate it as h(g(f(7))).

Front

What is the output of (f + g)(7) if f(7) = 19 and g(7) = -41?

Back

The output is f(7) + g(7) = 19 - 41 = -22.

Front

What is the formula for the composition of functions?

Back

The formula for the composition of functions is (f ∘ g)(x) = f(g(x)).

Front

What is the significance of parentheses in composite functions?

Back

Parentheses indicate the order of operations; the function closest to x is applied first.