Question

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.

Answer 1

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`