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