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

r(x) = x-1
s(x) = 3x^2
Write the expressions for (r+s) (x) and (r*s) (x) and evaluate (r-s) (-3).
(r+s) (x) =
(r*s) (x) =
(r-s) (-3) =

Please help.

1 Answer

3 votes
ANSWER

Given


r(x) = x - 1


and


s(x) = 3 {x}^(2)
ANSWER TO QUESTION 1


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



(r + s)(x) = x - 1 + 3 {x}^(2)



(r + s)(x) = 3 {x}^(2) + x - 1



ANSWER TO QUESTION 2




(r * s)(x) = r(x) * s(x)



(r * s)(x) = (x - 1) * 3 {x}^(2)



(r * s)(x) = 3 {x}^(3) - 3 {x}^(2)

ANSWER TO QUESTION 3


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




( r - s)(x) = x - 1 - 3 {x}^(2)



( r - s)( - 3) = (- 3) - 1 - 3 ({ - 3}^(2) )




( r - s)( - 3) = - 4 - 3 * 9




( r - s)( - 3) = - 4 - 27 = - 31

User Georg Leber
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