Function Operations & Compositions of Functions

Front

What are function operations?

Back

Function operations involve combining two or more functions using 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)).

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CCSS.HSF-BF.A.1C

Front

How do you determine if two functions are inverses?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

What is the formula for the product of two functions?

Back

The product of two functions f(x) and g(x) is given by (f ⋅ g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find (f + g)(x) for two functions?

Back

To find (f + g)(x), add the outputs of the two functions: (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

Evaluate f(x) = 3x^2 - 2x + 1 for f(2).

Back

f(2) = 3(2)^2 - 2(2) + 1 = 3(4) - 4 + 1 = 12 - 4 + 1 = 9.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

(f ⋅ g)(x) = f(x) * g(x) = 2x * (x + 3) = 2x^2 + 6x.

Tags

CCSS.HSF-BF.A.1B

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's expression.

Tags

CCSS.HSF.IF.A.2

Front

What is the sum of f(x) = x^2 and g(x) = 2x + 1?

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

What is the difference of two functions?

Back

The difference of two functions f(x) and g(x) is given by (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B