Function Operations and Composite 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 are function operations?

Back

Function operations include addition, subtraction, multiplication, and division of functions.

Tags

CCSS.HSF-BF.A.1B

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find f(x) / g(x)?

Back

To find f(x) / g(x), divide the output of function f by the output of function g for the same input x.

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = x^2 - 9 and g(x) = x + 3, what is f(x) / g(x)?

Back

f(x) / g(x) = x - 3.

Tags

CCSS.HSF-BF.A.1B

Front

How do you find g(f(x))?

Back

To find g(f(x)), substitute f(x) into g(x) and simplify.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is g(f(x))?

Back

g(f(x)) = 18x^2 - 84x + 90.

Tags

CCSS.HSF-BF.A.1C

Front

How do you find f(g(x))?

Back

To find f(g(x)), substitute g(x) into f(x) and simplify.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = -3x + 7 and g(x) = 2x^2 - 8, what is f(g(x))?

Back

f(g(x)) = -6x^2 + 31.

Tags

CCSS.HSF-BF.A.1C

Front

What is the result of f(n) - g(n) if f(n) = x^2 + 1 and g(n) = 2x - 5?

Back

f(n) - g(n) = x^2 - 2x + 6.

Tags

CCSS.HSF-BF.A.1B