233k views
2 votes
Express the given function h as a composition of two functions f and g, so that h(x) = (f ∘ g)(x). Formulate the question in an open-ended format.

1 Answer

0 votes

Final answer:

To express the given function h as a composition of two functions f and g, we need to find two functions that when composed together will give us h(x). We can express this composition as h(x) = f(g(x)).

Step-by-step explanation:

To express the function h as a composition of two functions f and g, we need to find two functions that when composed together will give us h(x). Let's say h(x) = (f ∘ g)(x). From this, we can see that f and g are functions that when applied to x in a specific order, will yield h(x). In other words, g is applied first to x, and then the result is passed to f. The composition can be written as h(x) = f(g(x)).

For example, let's say h(x) = (x^2 + 1)². We can express h as a composition of two functions f and g such that f(g(x)) = (x^2 + 1)².

Let's choose g(x) = x^2 + 1 and f(x) = x². Now, if we apply g(x) to x first, we get g(x) = (x^2 + 1). If we then apply f(x) to the result, we get h(x) = f(g(x)) = f(x^2 + 1) = (x^2 + 1)².

User MindStudio
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories