Function Operations & Compositions of Functions

Front

What is function composition?

Back

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

Front

How do you denote the sum of two functions?

Back

The sum of two functions f(x) and g(x) is denoted as (f + g)(x) = f(x) + g(x).

Front

What is the result of f(g(x)) if f(x) = 2x and g(x) = x^2 + 3?

Back

The result is f(g(x)) = 2(x^2 + 3) = 2x^2 + 6.

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(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, what is (f + g)(x)?

Back

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

Front

What is the composition of g(x) = 3x + 4 and h(x) = 3x - 1?

Back

The composition (g ∘ h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

Front

What is the difference between function addition and function composition?

Back

Function addition combines the outputs of two functions, while function composition applies one function to the output of another.

Front

How do you find f(g(x)) if f(x) is a polynomial?

Back

To find f(g(x)), substitute g(x) into every instance of x in the polynomial f(x).

Front

What is the output of f(g(x)) if f(x) = 3x - 16 and g(x) = x?

Back

The output is f(g(x)) = f(x) = 3x - 16.

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters; f(g(x)) is generally not the same as g(f(x)).