Question

What is (f⋅g)(x)?
f(x)=x²+2x−6

g(x)=x⁴+3

Answer 1

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.