find af gx b the domain of f g For fx 4x 9 and gx 1x Fi

find:

a.(f ? g)(x)

b. the domain of f ? g

For f(x) = 4/x + 9 and g(x) = 1/x Find: a.(f g)(x) b. the domain of f g

Solution

f(x) = 4/(x+9)

g(x) = 1/x

a) (f o g)(x) ; plug x = g(x) in f(x)

(f o g)(x) = 4/( 1/x +9) = 4x/( 1+9x)

b) Domain : 1+9x should not be zero

x = -1/9

So, Domain : ( - inf, -1/9)U (-1/9 , inf)