SOLUTION: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=2x+6 s(x)=3x write the expression for (r+s)(x),(r-s)(x) and evaluate (r*s)(-1)

Algebra ->  Functions -> SOLUTION: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=2x+6 s(x)=3x write the expression for (r+s)(x),(r-s)(x) and evaluate (r*s)(-1)      Log On


   

Question 1037635: Suppose that the functions r and s
are defined for all real numbers x
as follows.
r(x)=2x+6
s(x)=3x
write the expression for (r+s)(x),(r-s)(x) and evaluate (r*s)(-1)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is mostly about substitutions and doing simple arithmetic of functions.

Only doing the last part of the question,
r%28x%29%2As%28x%29=r%2As%28x%29
%282x%2B6%29%283x%29
6x%5E2%2B18x
-
Let x=-1.
6%28-1%29%5E2%2B18%28-1%29
6-18
highlight%28-12%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose that the functions r and s
are defined for all real numbers x
as follows.
r(x)=2x+6
s(x)=3x
write the expression for (r+s)(x),(r-s)(x) and evaluate (r*s)(-1)
(r * s)(- 1) means: r(- 1) * s(- 1)



r(x) = 2x + 6

r(- 1) = 2(- 1) + 6, or 4



s(x) = 3x

s(- 1) =3(- 1), or - 3



(r * s)(- 1) = r(- 1) * s(- 1) = 4(- 3) = highlight_green%28-+12%29