Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

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

Front

What does (f ° f)(x) mean?

Back

It means applying the function f to itself. For example, (f ° f)(x) = f(f(x)).

Front

If f(x) = 2x² - 1, what is (f ° f)(-2)?

Back

(f ° f)(-2) = f(f(-2)) = f(2(-2)² - 1) = f(7) = 2(7)² - 1 = 97.

Front

How do you find (f + g)(x) for two functions f(x) and g(x)?

Back

You add the two functions together: (f + g)(x) = f(x) + g(x).

Front

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

Back

(f + g)(x) = (3x² + 7x) + (2x² - x - 1) = 5x² + 6x - 1.

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f(g(x)) or (f ° g)(x).

Front

If f(x) = x - 5 and g(x) = 3x² - 1, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(3x² - 1) = (3x² - 1) - 5 = 3x² - 6.

Front

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

Back

(f + g)(x) is the sum of the functions, while (f ° g)(x) is the composition of the functions.