Operations and Composition of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

What does it mean to perform operations on functions?

Back

Performing operations on functions involves combining two or more functions using addition, subtraction, multiplication, or division.

Front

How do you add two functions?

Back

To add two functions f(x) and g(x), you compute (f + g)(x) = f(x) + g(x).

Front

How do you subtract two functions?

Back

To subtract two functions f(x) and g(x), you compute (f - g)(x) = f(x) - g(x).

Front

How do you multiply two functions?

Back

To multiply two functions f(x) and g(x), you compute (f * g)(x) = f(x) * g(x).

Front

How do you divide two functions?

Back

To divide two functions f(x) and g(x), you compute (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

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)).

Front

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

Back

To find f(g(x)), substitute g(x) into the function f wherever x appears.