Question

How do i findFind the domain of f ∘ g in the equation

Answer 1

First, we need to find the composite function of f ∘ g.

We need to write the function f(x) in terms of g(x).

Then:

`\begin{gathered} (fog)(x)=(6)/(g(x)+7)=(6)/(x+5+7) \\ =(6)/(x+12) \end{gathered}`

Now, to find the domain we need to look at the x values that the function can take.

The function is a rational function, then the domain is given using the denominator because it can be equal to zero.

x+12 = 0

x=-12

Therefore, the domain is the interval (-∞.-12)U(-12,∞)