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30 June, 18:27

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

+3
Answers (1)
  1. 30 June, 22:15
    0
    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
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