Compositions of Functions Math 8 Accelerated

Front

What is a composition of functions?

Back

A composition of functions is a process where one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is (g ∘ h)(x)?

Back

(g ∘ h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

When f(x) = 2x and g(x) = x² + 3, find f(g(x)).

Back

f(g(x)) = f(x² + 3) = 2(x² + 3) = 2x² + 6.

Front

What does (f ° g)(-1) represent?

Back

It represents the value of the function f applied to the result of g at -1, calculated as f(g(-1)).

Front

If f(x) = x - 5 and g(x) = 3x² - 1, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(3x² - 1) = (3x² - 1) - 5 = 3x² - 6.

Front

What is the output of f(g(5)) if g(x) = 3x + 4 and f(x) = x - 1?

Back

g(5) = 3(5) + 4 = 19; f(g(5)) = f(19) = 19 - 1 = 18.

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input from a set, often expressed as f(x).

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 f(x) = 2x + 1 and g(x) = x - 3, what is (f ∘ g)(2)?

Back

(f ∘ g)(2) = f(g(2)) = f(2 - 3) = f(-1) = 2(-1) + 1 = -2 + 1 = -1.

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.