Because this function is a polynomial, the domain is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mi mathvariant=¨normal¨»|«/mi»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«/mrow»«/mfenced»«/mstyle»«/math».


Again, as this is a polynomial, the domain is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mi mathvariant=¨normal¨»|«/mi»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«/mrow»«/mfenced»«/mstyle»«/math».

To find the domain of this composite function, find the restriction on the variable. There are two restrictions on the variable.

First, the value inside the radical cannot be less than zero.


The second restriction is that the denominator cannot equal zero.


Combining the two restrictions, the domain is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨normal¨»(«/mi»«mn»3«/mn»«mi mathvariant=¨normal¨»,«/mi»«mo»§#160;«/mo»«mo»§#8734;«/mo»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mstyle»«/math», or, in set builder notation, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»t«/mi»«mi mathvariant=¨normal¨»|«/mi»«mi»t«/mi»«mo»§#62;«/mo»«mn»3«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«/mrow»«/mfenced»«/mstyle»«/math».


To find the domain of this composite function, find the restrictions on the variable.

The value inside the radical cannot be less than zero.


In addition, the denominator cannot equal zero.


Combining the two restrictions, the domain is «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mfenced open=¨[¨»«mrow»«mn»0«/mn»«mi mathvariant=¨normal¨»,«/mi»«mo»§#160;«/mo»«mn»9«/mn»«/mrow»«/mfenced»«mo»§#8746;«/mo»«mfenced»«mrow»«mn»9«/mn»«mi mathvariant=¨normal¨»,«/mi»«mo»§#160;«/mo»«mo»§#8734;«/mo»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math», or, in set builder notation, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»t«/mi»«mi mathvariant=¨normal¨»|«/mi»«mi»t«/mi»«mo»§#8805;«/mo»«mn»0«/mn»«mi mathvariant=¨normal¨»,«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mo»§#8800;«/mo»«mn»9«/mn»«mi mathvariant=¨normal¨»,«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«/mrow»«/mfenced»«/mstyle»«/math».

Start by finding «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»g«/mi»«mfenced»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math».

 
Now, replace «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math» in «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mstyle»«/math» with «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»g«/mi»«mfenced»«mrow»«mi»h«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math».


Domain: «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mi mathvariant=¨normal¨»|«/mi»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»R«/mi»«/mrow»«/mfenced»«/mstyle»«/math»