Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

(f ° g)(2) = f(g(2)) = f(2 - 1) = f(1) = 2(1) + 3 = 5.

Front

What does g(f(2)) represent?

Back

g(f(2)) represents the value of function g applied to the result of function f evaluated at x = 2.

Front

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

Back

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

Front

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

Back

f(g(x)) applies g first and then f to the result, while g(f(x)) applies f first and then g to the result. They are generally not equal.

Front

If f(x) = x + 4 and g(x) = 2x, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(2x) = 2x + 4.

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. It is denoted as I(x) = x.

Front

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

Back

(f ° g)(3) = f(g(3)) = f(3^2) = f(9) = 9 - 1 = 8.

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 f(x) = 5x and g(x) = 2x - 1, what is (g ° f)(x)?

Back

(g ° f)(x) = g(f(x)) = g(5x) = 2(5x) - 1 = 10x - 1.