Compositions and Operations with 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 result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find f(g(x)) if f(x) = 2x and g(x) = x² + 3?

Back

To find f(g(x)), substitute g(x) into f: f(g(x)) = f(x² + 3) = 2(x² + 3) = 2x² + 6.

Tags

CCSS.HSF-BF.A.1C

Front

What is the sum of two functions?

Back

The sum of two functions f and g, denoted (f + g)(x), is defined as (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you evaluate (f + g)(2) if f(x) = 3x² + 1 and g(x) = 4x + 5?

Back

(f + g)(2) = f(2) + g(2) = (3(2)² + 1) + (4(2) + 5) = 26.

Tags

CCSS.HSF-BF.A.1B

Front

What is the notation for function composition?

Back

Function composition is denoted by (f ∘ g)(x) or f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate g[h(-2)] if h(x) = 3x + 4 and g(x) = 2x - 1?

Back

First, find h(-2): h(-2) = 3(-2) + 4 = -2. Then, find g(-2): g(-2) = 2(-2) - 1 = -5.

Tags

CCSS.HSF-BF.A.1C

Front

What is the output of g(4x) if g(x) = 3x + 4?

Back

g(4x) = 3(4x) + 4 = 12x + 4.

Tags

CCSS.HSF.IF.A.2

Front

What is the difference of two functions?

Back

The difference of two functions f and g, denoted (f - g)(x), is defined as (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find g(h(x)) if g(x) = 3x + 4 and h(x) = 2x - 1?

Back

To find g(h(x)), substitute h(x) into g: g(h(x)) = g(2x - 1) = 3(2x - 1) + 4 = 6x + 1.

Tags

CCSS.HSF-BF.A.1C