Final answer:
The composition (f⋅g)(x) of two functions is found by substituting g(x) into f(x). In this case, (f⋅g)(x) = x⁸ + 8x⁴ + 6x² + 9.
Step-by-step explanation:
The composition of two functions, f(x) and g(x), denoted as (f⋅g)(x), is found by substituting the function g(x) into the function f(x). In this case, f(x) = x² + 2x - 6 and g(x) = x⁴ + 3.
To find (f⋅g)(x), we replace x in f(x) with g(x).
Therefore, (f⋅g)(x) = f(g(x)) = (x⁴ + 3)² + 2(x⁴ + 3) - 6.
Expanding and simplifying the equation, we get (f⋅g)(x) = x⁸ + 6x⁴ + 9 + 2x⁴ + 6x² + 6 - 6 = x⁸ + 8x⁴ + 6x² + 9.