Question

Find the domain of fg

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


a. all real numbers

c. all real numbers, except -1

b. all real numbers, except 0

d. all real numbers, except 1

Answer 1

the correct answer is B

Explanation:

I took the test

Answer 2

We have the following functions:
f (x) = x ^ 2 + 1
g (x) = 1 / x
Multiplying we have:
(f * g) (x) = (x ^ 2 + 1) * (1 / x)
Rewriting:
(f * g) (x) = ((x ^ 2 + 1) / x)
Therefore, the domain of the function is given by all the values of x that do not make zero the denominator.
We have then:
All reals except number 0
Answer:
b. all real numbers, except 0