Write the expressions

Question

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

r(x) =x-5

s(x)=3x+5

write the expressions for (r+s)(x) and (r-s)(x) and evaluate (r•s)(-2).

Answer 1

r(x) = x-5

s(x) =3x+5

(r+s)(x) = x-5+3x+5= 4x

(r-s)(x) = x-5-3x-5= -2x-10

r(s(x)) = r(3x+5) = 3x+5-5 = 3x

r(s(-2)) = 3(-2) = -6

s(-2) =3(-2)+5 = -1

r(s(-2))=r(-1) = -1-5 = -6

r(x)s(x)=(x-5)(3x+5)=3x^2 -10x-25

r(-2)s(-2)=3(-2)^2 -10(-2)--25=-12+20-25= 7

r(-2)=-2-5= -7

s(-2)=3(-2)+5=-1

r(-2)s(-2)=-7(-1)=7