Function Composition

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) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

Back

g(h(x)) = 9x + 1.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for adding two functions f and g?

Back

(f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = 3x^2 + 1 and g(x) = 4x + 5, what is (f + g)(2)?

Back

(f + g)(2) = 26.

Tags

CCSS.HSF-BF.A.1B

Front

What is the result of g(f(x)) if f(x) = x - 1 and g(x) = 2x?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate f(x - 2) if f(x) = 2x^2 - 5x + 12?

Back

f(x - 2) = 2(x - 2)^2 - 5(x - 2) + 12 = 2x^2 - 13x + 18.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

f(g(5)) = 19.

Tags

CCSS.HSF-BF.A.1C

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g.

Tags

CCSS.HSF-BF.A.1C

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.

Front

What is the composition of the identity function with another function f?

Back

(I ∘ f)(x) = f(x) and (f ∘ I)(x) = f(x).

Tags

CCSS.HSF-BF.A.1C