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. If f and g are two functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find g(f(x)) if g(x) = x^2 + 6 and f(x) = 2x - 4?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = g(2x - 4) = (2x - 4)^2 + 6 = 4x^2 - 16x + 22.

Front

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

Back

The result of (f + g)(x) is f(x) + g(x) = 2x + 3x = 5x.

Front

What is the composition f(g(x)) if f(x) = 5x and g(x) = 2x - 1?

Back

To find f(g(x)), substitute g(x) into f: f(g(x)) = f(2x - 1) = 5(2x - 1) = 10x - 5.

Front

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

Back

f(g(x)) applies function g first and then applies function f to the result, while g(f(x)) applies function f first and then applies function g.

Front

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

Back

g(f(1)) = g(1 + 3) = g(4) = 2(4) = 8.

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

How do you express the composition of functions algebraically?

Back

The composition of functions f and g can be expressed as (f ∘ g)(x) = f(g(x)).

Front

What is the domain of the composition of 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 and g(x) = x + 1, what is (f ∘ g)(x)?

Back

(f ∘ g)(x) = f(g(x)) = f(x + 1) = (x + 1)^2 = x^2 + 2x + 1.