Question

find the domain of fg

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


a. all real numbers

c. all real numbers, except -2


b. all real numbers, except 2

d. (-2, 0) U [2, -2)

Answer 1

We have the following functions:
 f (x) = x + 2
 g (x) = 1 / x + 2
 Multiplying we have:
 (f * g) (x) = (x + 2) * (1 / x + 2)
 Rewriting:
 (f * g) (x) = (x + 2 / x + 2)
 (f * g) (x) = 1
 Therefore, the domain of the function is any real number.
 Answer:
 a. all real numbers