Question

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

Answer 1

a) ( r+ s) (x) = 3 x + 9

b) ( r . s ) (x) = 2 x² + 13 x +20

c) ( r- s) (x) = -1 -x

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