Question

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to mc001-1.jpg?

Answer 1

Thank you for asking this question. Here is your answer.

(f*g)(x) = f(x)*g(x)

 You are given f(x) = 3x + 2 and g(x) = x^2 + 1. Simply substitute these expressions as follows:

  f(x)*g(x) = (3x + 2)*(x^2 + 1)

 

  (3x + 2)*(x^2 + 1) = (3x)(x^2) + (3x)(1) + (2)(x^2) + (2)(1) <-- the foil method

                               =     3x^3    +     3x    +   2x^2    +    2     <-- simplify each term

                               = 3x^3 + 2x^2 + 3x + 2  

If there is any confusion please leave a comment below.