4 Let x and gx lxl a Find f g00x02 points b Find fg00x point

4) Let x and g(x) lxl a. Find (f +g00x02 points) b. Find (f-g00x) points) c. Find (f.gx )(2 points) id. Find (x) (2 points) e. Bonus: (8 points) Using the piecewise definition of xl re-write parts a-d as niecewise functions.

Solution

f(x) = x ; g(x) =|x|

a) (f+g)(x) : add the two functions

(f+g)(x) = x+ |x|

x=2 ; (f +g)(x) = 2 +|2| = 4

b) ( f- g)(x) = x - |x|

x=2 ; ( f- g)(2) = 2 - |2| =0

c) (f*g)(x) = f(x)*g(x) = x|x|

x=2 ; (f*g)(x) = 2|2| = 4

d) (f/g)(x) = x/|x|

x=2 (f/g)(x) = 2/|2| = 1