Function Operations and Composite Functions Review

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.

Front

Define composite function.

Back

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

Front

What is the notation for function multiplication?

Back

The notation for function multiplication is (f * g)(x) = f(x) * g(x).

Front

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

Back

To find f(g(x)), substitute g(x) into the function f wherever there is an x.

Front

What is the result of f(x) = x^2 and g(x) = 3x when finding g(f(x))?

Back

g(f(x)) = g(x^2) = 3(x^2) = 3x^2.

Front

Evaluate f(x) = 2x + 3 for f(4).

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

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

Back

f(x) and g(x) are two different functions that can be combined through operations like addition, subtraction, multiplication, or composition.

Front

If f(x) = x^3 - 3x, what is f(2)?

Back

f(2) = 2^3 - 3(2) = 8 - 6 = 2.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if they produce the same output for every input in their domain.

Front

How do you evaluate g(f(x)) if g(x) = -4x + 1?

Back

Substitute f(x) into g: g(f(x)) = -4(f(x)) + 1.