Answer
$(f \cdot g)(x) = f(x) \cdot g(x) = 3x^3 - 2x^2 + 3x - 2$
Work Step by Step
This exercise asks us to multiply the two functions together. Let's write out the problem:
$(f \cdot g)(x) = f(x) \cdot g(x) = (3x - 2)(x^2 + 1)$
Use the FOIL method to distribute the terms:
$(f \cdot g)(x) = f(x) \cdot g(x) = (3x)(x^2) + (3x)(1) + (-2)(x^2) + (-2)(1)$
Multiply to simplify:
$(f \cdot g)(x) = f(x) \cdot g(x) = (3x^3) + (3x) - (2x^2) - (2)$
Rewrite in a more conventional form in terms of decreasing powers:
$(f \cdot g)(x) = f(x) \cdot g(x) = 3x^3 - 2x^2 + 3x - 2$
