Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function, denoted as (f ◦ g)(x) = f(g(x)).

Front

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

Back

(f ◦ g)(x) = f(g(x)) = f(x - 1) = 2(x - 1) + 3 = 2x - 2 + 3 = 2x + 1.

Front

What does (f + g)(x) represent?

Back

(f + g)(x) represents the sum of two functions f(x) and g(x), calculated as (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 and g(x) = 3x, what is (f + g)(x)?

Back

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

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 g(x) = 3x + 4, what is g(2)?

Back

g(2) = 3(2) + 4 = 6 + 4 = 10.

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. They are generally not equal.

Front

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

Back

(g ◦ f)(x) = g(f(x)) = g(x + 1) = 2(x + 1) = 2x + 2.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input, denoted as I(x) = x.

Front

If f(x) = x^2 and g(x) = x + 2, what is (f ◦ g)(2)?

Back

(f ◦ g)(2) = f(g(2)) = f(2 + 2) = f(4) = 4^2 = 16.