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

a)  ( r+ s) (x)  = 3 x + 9

b)   ( r . s ) (x) =  2 x² + 13 x +20

c) ( r- s) (x)  = -1 -x

Step-by-step explanation:

Step(i):-

Given that r(x) = x +4 and s(x) =  2x + 5

a)   ( r+ s) (x)  = r(x) + s(x)

                    = x +4 + 2x +5

                   = 3 x + 9

    ( r+ s) (x)  = 3 x + 9

b)

    ( r . s ) (x)  = r(x) . s(x)

                    = (x+4) . ( 2x +5)

                   = x ( 2x +5) + 4( 2x +5)

                  = 2 x² + 5 x + 8 x +20

                 = 2 x² + 13 x +20

( r . s ) (x) =  2 x² + 13 x +20

c)

 ( r- s) (x)  = r(x) - s(x)

               =  (x+4 - ( 2x +5)

              = x +4 - 2x -5

            = -x -1

( r- s) (x)  = -1 -x