Question

Find two functions, f(x) and g(x), such that (f o g)(x) = h(x)?

Answer 1

To find two functions, f(x) and g(x), such that (f o g)(x) = h(x), we can compose the functions by plugging g(x) into f(x).

Step-by-step explanation:

In general, to find two functions, f(x) and g(x), such that (f o g)(x) = h(x), we need to compose the functions in a specific order. Let's say h(x) = (f o g)(x), then g(x) could be a function that transforms x into another variable, let's call it t. Then we can define f(t) as h(x). So, g(x) -> t, and f(t) = h(x).

For example, let's take f(x) = x^2 and g(x) = x + 1. Now we can find (f o g)(x) as follows:

1. Plug g(x) into f(x): f(g(x)) = (x + 1)^2 = x^2 + 2x + 1
2. Therefore, h(x) = x^2 + 2x + 1