Final answer:
To find the composition (h∘g)(x), we evaluate g(x), which is x², and then use it as the input for h(x), which gives us r(x) = x⁸.
Step-by-step explanation:
The question asked is to find r(x), which is represented by (h∘g)(x). This is a composition of two functions where h(x) = x⁴ and g(x) = x². To find the composition (h∘g)(x), we start by evaluating g(x) and then applying the result as the input to h(x).
Firstly, consider g(x) = x². Now, we need to plug this into h, so we get:
h(g(x)) = h(x²), which is simply applying the value from g(x) into h(x).
Next, we substitute x² into h(x) to get h(x²) = (x²)⁴. By the properties of exponents, we know that when raising a power to a power, we multiply the exponents, thus (x²)⁴ = x⁴² = x⁸.
Therefore, the composition (h∘g)(x) results in r(x) = x⁸.