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 find g(f(x))?

Back

To find g(f(x)), substitute f(x) into g(x). This means you take the output of f(x) and use it as the input for g.

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find g(f(x)).

Back

g(f(x)) = 18x² - 84x + 90.

Front

What is the value of f(-2) if f(x) = x + 3?

Back

f(-2) = 1.

Front

How do you evaluate f(x) at a specific point?

Back

To evaluate f(x) at a specific point, substitute the value of x into the function and simplify.

Front

Given f(x) = 2x² + 5x - 17, find f(-1).

Back

f(-1) = -20.

Front

Given f(x) = 2x and g(x) = x² + 3, find f(g(x)).

Back

f(g(x)) = 2x² + 6.

Front

What is the process to find f(g(x))?

Back

To find f(g(x)), substitute g(x) into f(x). This means you take the output of g(x) and use it as the input for f.

Front

Given f(x) = -3x + 7 and g(x) = 2x² - 8, find f(g(x)).

Back

f(g(x)) = -6x² + 31.

Front

What is the significance of composite functions in mathematics?

Back

Composite functions allow us to combine different functions to create new functions, which can simplify complex problems and model real-world scenarios.