Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find f(g(x)) for given functions f and g?

Back

To find f(g(x)), substitute g(x) into the function f. This means you take the output of g(x) and use it as the input for f.

Tags

CCSS.HSF-BF.A.1C

Front

What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

The result is 19.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

g(f(x)) = 2(x - 1) = 2x - 2.

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate f(-1) if f(x) = 2x^2 + 5x - 17?

Back

Substitute -1 into the function: f(-1) = 2(-1)^2 + 5(-1) - 17 = -20.

Tags

CCSS.HSF.IF.A.2

Front

What is the composition f(g(x)) if f(x) = 5x and g(x) = 2x - 1?

Back

f(g(x)) = f(2x - 1) = 5(2x - 1) = 10x - 5.

Tags

CCSS.HSF-BF.A.1C

Front

How do you find (g∘h)(x) for g(x) = 3x + 4 and h(x) = 3x - 1?

Back

To find (g∘h)(x), substitute h(x) into g: (g∘h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

Tags

CCSS.HSF-BF.A.1C

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)).

Tags

CCSS.HSF-BF.A.1C

Front

What is the domain of the 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.

Tags

CCSS.HSF-BF.A.1B

Front

What is the range of the composition of functions?

Back

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

Tags

CCSS.HSF-BF.A.1C