Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=x-5 s(x)=2x+6 Write the expressions for (r*s)(x) and (r-s)(x) and evalu

Question

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

 

r(x)=x-5

s(x)=2x+6

 

Write the expressions for (r*s)(x) and (r-s)(x) and evaluate (r+s)(3)

Answer 1

(r*s) = (x-5)(2x+6) = 2x² + 6x - 10x - 30 = 2x² - 4x - 30

(r-s)(x) = x-5 - (2x+6) = x - 5 - 2x - 6 = -x - 11

(r+s)(x) = x - 5 + 2x + 6 = 3x + 1

(r + s)(3) = 3(3) + 1 = 9 + 1 = 10