For f xx 2 and gx 3 x find a fgx b fgx c fgx d fgx and the d

For f (x)=?x+ 2 and g(x)= 3-? x find

a) (f+g)(x)

b) (f-g)(x)

c) (fg)(x)

d) (f/g)(x)

and the domain for each.

We have been given that f(x) = x+ 2 and g(x) = 3 - x

a) (f + g)(x) = f(x) + g(x) = (x+ 2 ) + (3 -x)

b) (f - g)(x) = f(x) - g(x) = (x+ 2) - (3 -x) = (x+ 2) + x - 3

c) (fg)(x) = f(x)g(x) = [(x+ 2](3-x) However fog (x) = f [g(x)] = f [ ( 3- x)] = { (3 - x) + 2} = ( 5 - x)

d) (f /g)(x) = f(x) / g(x) = [(x+ 2] / ( 3 -x)

e) (f X g)(x) = f(x) X g(x) = [(x+ 2)] ( 3 - x)

f) (g X f )(x) = g (x) X f(x) = (3 -x) [ (x+ 2) ]

NOTE: fog denotes a composite function i.e. (f og)(x) = f [ g(x)] . Also (fg )(x) =( f X g)(x)