Function Composition

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f and g are two functions, the composition of f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as (f ∘ g)(x).

Front

What is the result of f(g(x)) if f(x) = x^2 and g(x) = x + 1?

Back

The result is (g(x))^2 = (x + 1)^2 = x^2 + 2x + 1.

Front

If f(x) = 2x and g(x) = x - 3, what is f(g(5))?

Back

f(g(5)) = f(5 - 3) = f(2) = 2 * 2 = 4.

Front

What is the value of g(f(2)) if f(x) = x + 1 and g(x) = 3x?

Back

g(f(2)) = g(2 + 1) = g(3) = 3 * 3 = 9.

Front

What is the domain of the composition of two functions?

Back

The domain of the composition f(g(x)) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

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

Back

(f ∘ g)(3) = f(g(3)) = f(2 * 3) = f(6) = 6^2 - 1 = 35.

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 can yield different results.

Front

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

Back

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

Front

What is the composition of the identity function with another function?

Back

The composition of the identity function I(x) = x with any function f is I(f(x)) = f(x) and f(I(x)) = f(x).