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

How Do I FindFind The Domain Of F G In The Equation class=

Sagot :

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:

[tex]\begin{gathered} (fog)(x)=\frac{6}{g(x)+7}=\frac{6}{x+5+7} \\ =\frac{6}{x+12} \end{gathered}[/tex]

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,∞)

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