Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way of 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

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

Back

(g ∘ f)(x) = g(f(x)) = g(3x - 1) = (3x - 1)^2 + 2 = 9x^2 - 6x + 3.

Front

If w(x) = -3x + 9 and g(x) = 5x - 7, find (w ∘ g)(x).

Back

(w ∘ g)(x) = w(g(x)) = w(5x - 7) = -3(5x - 7) + 9 = -15x + 30.

Front

What does f(x - 2) represent?

Back

f(x - 2) represents the function f evaluated at (x - 2), which shifts the graph of f horizontally to the right by 2 units.

Front

If f(x) = √(x + 5) - 1 and g(x) = 4x - 3, find (f ∘ g)(x).

Back

(f ∘ g)(x) = f(g(x)) = f(4x - 3) = √(4x - 3 + 5) - 1 = √(4x + 2) - 1.

Front

If h(x) = 3x - 1 and f(x) = x^2 + 2, what is (h ∘ f)(x)?

Back

(h ∘ f)(x) = h(f(x)) = h(x^2 + 2) = 3(x^2 + 2) - 1 = 3x^2 + 5.

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

How do you evaluate (f ∘ g)(x) if f(x) = 2x + 3 and g(x) = x^2?

Back

(f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3.

Front

What is the domain of the composition of functions?

Back

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

Front

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

Back

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