Composition Functions: Graphs, Tables, and Applications

Front

What is a composition of functions?

Back

A composition of functions is a function that is created by applying one function to the results of another function, denoted as (f ° g)(x) = f(g(x)).

Front

How do you calculate (f ° f)(x) for f(x) = 2x^2 - 1?

Back

To calculate (f ° f)(x), substitute f(x) into itself: f(f(x)) = f(2x^2 - 1) = 2(2x^2 - 1)^2 - 1.

Front

What is the value of (f ° f)(-2) for f(x) = 2x^2 - 1?

Back

The value is 97.

Front

What does the notation (f ° g)(x) represent?

Back

It represents the composition of functions f and g, meaning you first apply g to x, then apply f to the result.

Front

If f(x) = 2x and g(x) = 2x^2 - 1, what is f(g(x))?

Back

f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.

Front

What is the result of f(g(1)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

g(1) = 1, then f(g(1)) = f(1) = 2.

Front

How do you find h(f(-1)) if h(x) is another function?

Back

First, calculate f(-1), then substitute that result into h.

Front

What is the value of h(f(-1)) if f(-1) = 4?

Back

The value is -4.

Front

If h(f(-2)) = 2, what does this imply about the functions h and f?

Back

It implies that when you input -2 into f, the output is such that h of that output equals 2.

Front

What is the significance of the output of a composition of functions?

Back

The output of a composition of functions gives the result of applying one function after another, which can represent real-world scenarios.