Question

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.

Answer 1

hey there hope this answer helps you out

Explanation:

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

`f(x) = (1)/(x)`

and

`g(x) = {x}^(2) + 6x`

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

`fog = (1)/(g(x))`

`fog \: = \frac{1}{ {x}^(2) + 6x }`

taking x common in denominator

`fog = (1)/(x(x + 6))`

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