sum, difference, and product of two functions

Question

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

r(x)=3x-6

s(x)=6x

 

write the expressions for

(r - s)(x)=____

(r + s)(x)=____

(r * s)(-1)=____

Answer 1

r(x) = 3x - 6

s(x) = 6x

 

(r-s)(x) = r(x)-s(x) = 3x - 6 - 6x = ______?

 

(r+s)(x) = r(x) + s(x) = 3x - 6 + 6x = _______?

 

(r·s)(x) = r(x)·s(x) = (3x - 6)(6x) = _______?

Answer 2

R-S =  3x-6 - 6x = -3x - 6 = -3(x+2)

 

R +S = 9x - 6

 

R*s = 18x^2 - 36x

 

R*s(-1) = 18(-1)^2 - 36(-1) = 18(1) + 36 = 54

R(-1) = 3(-1)-6 = -3-6 = -9 and S(-1) = -6  and -9 * -6 = 54