Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ° g)(x), is the process of applying one function to the results of another function. It means substituting the output of g(x) into f(x).

Front

If f(x) = 3x - 1 and g(x) = x² + 2, what is (f ° g)(x)?

Back

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

Front

For 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

If g(x) = 3x + 4 and h(x) = 3x - 1, find (g ∘ h)(x).

Back

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

Front

If f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

g(5) = 5 - 2 = 3; f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f ° g)(x), which means f(g(x)).

Front

What is the domain of a composition of functions?

Back

The domain of (f ° g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

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

Back

(f ° g)(x) = f(g(x)) = f(2x) = 2x + 1.

Front

What is the range of the function f(x) = x²?

Back

The range of f(x) = x² is [0, ∞) since the output is always non-negative.

Front

If f(x) = x - 3, what is f(0)?

Back

f(0) = 0 - 3 = -3.