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GET 95 POINTS Let f(x) = 1/x and g(x)=x² + 6x. What
two numbers are not in the domain of fᵒg?
Separate your answers with a comma.

GET 95 POINTS Let fx 1x and gxx 6x What two numbers are not in the domain of fᵒg Separate your answers with a comma class=

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Answer:

hey there hope this answer helps you out

Step-by-step explanation:

we have two functions f(x) and g(x) such that

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} + 6x[/tex]

solving for f ° g, we'll substitute the x in f(x) by the value of g(x)

[tex]fog = \frac{1}{g(x)} [/tex]

[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]

taking x common in denominator

[tex]fog = \frac{1}{x(x + 6)} [/tex]

for a function to exist it should not have 0 in its denominator

checking the values of x for which the denominator of f ° g becomes 0 :-

  • x = 0 and
  • x = -6

so the function doesn't exist at values x = 0, -6

So, 0, -6 cannot be in the domain of f°g

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