Question

Suppose that the functions r and s are defined for all real numbers x as follows:

r(x) = 2x - 6
s(x) = 6x
Write the expressions for (r-s)(x) and (r+s)(x) and evaluate (r-s)(2).

Answer 1

The expressions for (r-s)(x) and (r+s)(x) are -4x - 6 and 8x - 6 respectively. Evaluating (r-s)(2) yields -14.

Step-by-step explanation:

The question involves finding expressions for the combined functions of (r-s)(x) and (r+s)(x), and then evaluating (r-s) at x=2. Given r(x) = 2x - 6 and s(x) = 6x, we can derive these expressions through basic function operations.

For (r-s)(x), we subtract the function s from r:

(r-s)(x) = r(x) - s(x)

(r-s)(x) = (2x - 6) - (6x) = -4x - 6

For (r+s)(x), we add the functions r and s together:

(r+s)(x) = r(x) + s(x)

(r+s)(x) = (2x - 6) + (6x) = 8x - 6

To evaluate (r-s)(2), we substitute x with 2:

(r-s)(2) = -4(2) - 6 = -14