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Please help me on my question It’s all one question

Please help me on my question It’s all one question-example-1
User AchrafBj
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1 Answer

2 votes

It is given that:


f(x)=(2)/(x);g(x)=3x+12

1) f(g(x)) will be:


f(g(x))=(2)/(g(x))=(2)/(3x+12)

2)The domain will be all real numbers except x=-4.


\text{Domain of f(g(x))=(-}\infty,-4)\cup(-4,\infty)

3)g(f(x)) will be:


\begin{gathered} g(f(x))=3f(x)+12 \\ =3((2)/(x))+12 \\ =(6+12x)/(x) \end{gathered}

4) The domain of g(f(x)) is:


(-\infty,0)\cup(0,\infty)

5) f(f(x)) is given by:


f(f(x))=(2)/(f(x))=(2)/((2)/(x))=x

6)The domain of f(f(x)) is:


(-\infty,\infty)

7) g(g(x)) is calculated as:


\begin{gathered} g(g(x))=3(g(x))+12=3(3x+12)+12 \\ =9x+36+12 \\ =9x+48 \end{gathered}

8)The domain of g(g(x)) is:


(-\infty,\infty)

User Malgosia
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