Question

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

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



$(r \times s)(x) = r(x) \times s(x)$


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


$(r \times s)(x) = 3 {x}^{3} - 3 {x}^{2}$

ANSWER TO QUESTION 3

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



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


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



$( r - s)( - 3) = - 4 - 3 \times 9$



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