Suppose that the functions r and s are defined for all real

Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 2x - 6 s(x) = x+4 Write the expressions for (s + r)(x) and (s middot r)(x) and evaluate (s - r)(l).

Solution

s(x) = x + 4 ; r(x) = 2x -6

(s +r)(x) : just add the two functions

(s+r)(x) = x+ 4 +2x -6 = 3x -2

(s.r)(x ; multiply the two functions

= (x+4)(2x -6)

= 2x^2 +2x -24

( s- r)(x) : subtract the two functions

= ( x +4 -2x +6)

= -x +10

Now ( s -r)(1) = -1 +10 = 9