Function Operations & Compositions of Functions

Front

Define function operations.

Back

Function operations refer to the mathematical processes of combining two or more functions through addition, subtraction, multiplication, or division.

Tags

CCSS.HSF-BF.A.1B

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f∘g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

Find (g∘h)(x) if g(x)=3x+4 and h(x)=3x-1.

Back

(g∘h)(x) = g(h(x)) = g(3x-1) = 3(3x-1) + 4 = 9x - 3 + 4 = 9x + 1.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for (f + g)(x)?

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

Tags

CCSS.HSF-BF.A.1B

Front

How do you evaluate f(g(0))?

Back

First, find g(0), then substitute that value into f(x).

Tags

CCSS.HSF-BF.A.1C

Front

Evaluate f(-1) for f(x)=x^2-2x+1.

Back

f(-1) = (-1)^2 - 2(-1) + 1 = 1 + 2 + 1 = 4.

Tags

CCSS.HSF.IF.A.2

Front

What is the formula for (f⋅g)(x)?

Back

(f⋅g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

Given f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, find (f⋅g)(x).

Back

(f⋅g)(x) = (3x^2 - 2x + 1)(x - 4) = 3x^3 - 14x^2 + 9x - 4.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1B