Flashcard Function Composition and Evaluation

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the sum of two functions?

Back

To find the sum of two functions f(n) and g(n), you add their outputs: (f + g)(n) = f(n) + g(n).

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

If f(n) = n^2 + 4n and g(n) = -n - 5, what is f(n) + g(n)?

Back

f(n) + g(n) = n^2 + 4n - n - 5 = n^2 + 3n - 5.

Front

What does g(f(1)) mean?

Back

g(f(1)) means you first find f(1) and then use that result as the input for g.

Front

If f(n) = 2n + 1 and g(n) = 3n, what is f(n) + g(n)?

Back

f(n) + g(n) = (2n + 1) + (3n) = 5n + 1.

Front

What is the product of two functions?

Back

The product of two functions f(x) and g(x) is denoted as (f ⋅ g)(x) = f(x) * g(x).

Front

If f(x) = 4x + 1 and g(x) = 5x - 2, what is (f ⋅ g)(x)?

Back

(f ⋅ g)(x) = (4x + 1)(5x - 2) = 20x^2 - 3x - 2.

Front

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

Back

f(g(x)) means you apply g first and then f, while g(f(x)) means you apply f first and then g.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.