Composition of 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.

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

If g(x) = 2x + 1, what is g(3)?

Back

g(3) = 2(3) + 1 = 7.

Front

If f(x) = x^2, what is f(g(2)) if g(x) = x + 1?

Back

g(2) = 2 + 1 = 3; f(g(2)) = f(3) = 3^2 = 9.

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

If f(x) = 3x - 4, what is f(1)?

Back

f(1) = 3(1) - 4 = -1.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f ∘ g)(x), which means f(g(x)).

Front

If h(x) = x^2 + 1, what is h(-4)?

Back

h(-4) = (-4)^2 + 1 = 16 + 1 = 17.

Front

What is an example of a function that is not one-to-one?

Back

An example of a function that is not one-to-one is f(x) = x^2, since both f(2) and f(-2) yield the same output (4).