Function Operations and Composite Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What are function operations?

Back

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

Front

How do you add two functions f(x) and g(x)?

Back

To add two functions, you combine their outputs: (f + g)(x) = f(x) + g(x).

Front

How do you subtract two functions f(x) and g(x)?

Back

To subtract two functions, you find the difference of their outputs: (f - g)(x) = f(x) - g(x).

Front

How do you multiply two functions f(x) and g(x)?

Back

To multiply two functions, you multiply their outputs: (f ⋅ g)(x) = f(x) * g(x).

Front

How do you divide two functions f(x) and g(x)?

Back

To divide two functions, you divide their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function: (f ∘ g)(x) = f(g(x)).

Front

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

Back

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

Front

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

Back

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

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) for which the function is defined.