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

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