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

How do you find f(g(x)) for given functions f and g?

Back

To find f(g(x)), substitute g(x) into the function f. This means you take the output of g(x) and use it as the input for f.

Front

What is the result of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

The result is 19.

Front

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

Back

g(f(x)) = 2(x - 1) = 2x - 2.

Front

How do you evaluate f(-1) if f(x) = 2x^2 + 5x - 17?

Back

Substitute -1 into the function: f(-1) = 2(-1)^2 + 5(-1) - 17 = -20.

Front

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

Back

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

Front

How do you find (g∘h)(x) for g(x) = 3x + 4 and h(x) = 3x - 1?

Back

To find (g∘h)(x), substitute h(x) into g: (g∘h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

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

What is the domain of the composition of functions?

Back

The domain of (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

What is the range of the composition of functions?

Back

The range of (f ∘ g)(x) is the set of all possible outputs of f(g(x)).