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) = x - 5, what is f(3)?

Back

f(3) = 3 - 5 = -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

How do you find (f ° g)(x) if f(x) = x - 5 and g(x) = 3x² - 1?

Back

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

Front

What is the value of f(f(3)) if f(x) = x - 5?

Back

f(f(3)) = f(-2) = -2 - 5 = -7.

Front

If p(x) = 3x + 4, what is p(-3)?

Back

p(-3) = 3(-3) + 4 = -9 + 4 = -5.

Front

What is the result of p(p(-3)) if p(x) = 3x + 4?

Back

p(p(-3)) = p(-5) = 3(-5) + 4 = -15 + 4 = -11.

Front

If h(x) = 2x + 1, what is h(f(-1)) if f(x) = x - 5?

Back

f(-1) = -1 - 5 = -6; h(-6) = 2(-6) + 1 = -12 + 1 = -11.

Front

What is the domain of the composition of functions?

Back

The domain of the composition of functions 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

What is the range of the composition of functions?

Back

The range of the composition of functions f(g(x)) is the set of all possible outputs of f(g(x)).