Composition of Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Tags

CCSS.8.F.A.1

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

g(f(2)) = g(2*2 + 3) = g(7) = 7 - 1 = 6.

Tags

CCSS.HSF-BF.A.1C

Front

What is the notation for function composition?

Back

The notation for function composition is (f ∘ g)(x), which means f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find (f ∘ g)(x) if f(x) = x^2 and g(x) = 3x + 1?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

If f(x) = 3x + 2, what is f(0)?

Back

f(0) = 3(0) + 2 = 2.

Tags

CCSS.HSF.IF.A.2

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, leading to different results.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

h(g(3)) = h(3^2) = h(9) = 9 + 1 = 10.

Tags

CCSS.HSF-BF.A.1C