L1.7 Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

(f ° g)(x) = 3x² - 6.

Front

If f(x) = x - 1 and g(x) = 2x, what is g(f(x))?

Back

g(f(x)) = 2x - 2.

Front

If f(x) = 5x and g(x) = 2x - 1, what is the composition f(g(x))?

Back

f(g(x)) = 10x - 5.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f(g(x)) or (f ° g)(x).

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, find (g ∘ h)(x).

Back

(g ∘ h)(x) = 9x + 1.

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions is defined as (f + g)(x) = f(x) + g(x).

Front

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x² + 6x - 1.

Front

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

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g.

Front

If f(x) = x² and g(x) = x + 1, what is (f ° g)(x)?

Back

(f ° g)(x) = (x + 1)² = x² + 2x + 1.