Final answer:
To find (f\u00b7g)(x), multiply f(x) = x² + 2x - 6 by g(x) = x⁴ + 3, which results in the product 2x⁵ - 6x⁴ + 3x² + 6x - 18.
Step-by-step explanation:
The student has asked the question, "What is (f\u00b7g)(x)?" where f(x) is given as x² + 2x - 6 and g(x) is given as x⁴ + 3. To find (f\u00b7g)(x), we need to multiply the function f(x) by the function g(x).
The multiplication process involves expanding the product by using the distributive property, which means multiplying each term in the first function by each term in the second function.
Here's the calculation step by step:
Combining these results, you get:
(f\u00b7g)(x) = x¶ + 3x² + 2x⁵ + 6x - 6x⁴ - 18
Now, you simplify and combine like terms:
(f\u00b7g)(x) = x⁵ + (3x² - 6x⁴) + 2x⁵ + 6x - 18
Simplified further, this becomes:
(f\u00b7g)(x) = 2x⁵ - 6x⁴ + 3x² + 6x - 18
Therefore, the product of f(x) and g(x) is 2x⁵ - 6x⁴ + 3x² + 6x - 18.