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.