Question

Suppose That The Functions R And S Are Defined For All Real Numbers X As Follows.

R(X)=3x2
S(X)=X−4
Write The Expressions For (r⋅s)(x) and (r+s)(x) and evaluate (r−s)(3).

Answer 1

The expressions for (r⋅s)(x) and (r+s)(x) are 3x^3 - 12x^2 and 3x^2 + x - 4, respectively. To evaluate (r−s)(3), substitute x=3 into the expression and simplify to get 28.

Step-by-step explanation:

The expressions for (r⋅s)(x) and (r+s)(x) can be found by substituting the given functions R(x) and S(x) into the respective operations:

(r⋅s)(x) = R(x) ⋅ S(x) = (3x^2) ⋅ (x-4) = 3x^3 - 12x^2

(r+s)(x) = R(x) + S(x) = (3x^2) + (x-4) = 3x^2 + x - 4

To evaluate (r−s)(3), we substitute x=3 into the expression:

(r−s)(3) = R(3) - S(3) = (3(3)^2) - (3-4) = 3(9) - (-1) = 27 + 1 = 28