Final answer:
To calculate (f⋅g)(x), multiply f(x) = x² + 2x − 6 and g(x) = x⁴ + 3, then simplify the expression to get (f⋅g)(x) = x⁶ + 2x⁵ − 6x⁴ + 3x² + 6x − 18.
Step-by-step explanation:
The question asks us to find the product of two functions, f(x) and g(x).
Given:
f(x) = x² + 2x − 6
g(x) = x⁴ + 3
To find (f⋅g)(x), we multiply f(x) by g(x):
(f⋅g)(x) = (x² + 2x − 6)(x⁴ + 3)
Now, we expand this expression by using the distributive property:
(f⋅g)(x) = x²(x⁴) + 2x(x⁴) − 6(x⁴) + 3(x²) + 6x − 18
Simplifying the expression, we get:
(f⋅g)(x) = x⁶ + 2x⁵ − 6x⁴ + 3x² + 6x − 18
This final expression represents the answer to the student's question.