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If f x equals x -3 + g x equals 1 - x 2 - 9 find ( f og) (x and give any restrictions on its domain

User Sagar Jha
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\begin{gathered} f(x)=x-3 \\ g(x)=(1)/(x^2-9) \\ (\text{fog)(x)}=(1)/(x^2-9)-3 \end{gathered}

the denominator cannot be zero, because the division by zero is not defined, therefore:


\begin{gathered} x^2-9=0 \\ \text{Solving for x:} \\ x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}

Therefore the domain of (f o g)(x) is:


D\colon(-\infty,-3)\cup(-3,3)\cup(3,\infty)

User Matt Hill
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