168 L13 Composite Functions; One-to-one Functions; Inverse Functions A compositefunction fgD(read as “fcomposed with g”) is defined by ()( )(( ))fgxf g x=D. The domain of fgDis the set of all real xin the domain of gfor which ()g xis in the domain of f. Example: Show a diagram for the composite function ()( )(( ))fgxf g x=DSimilarly we define: ()( )(( ))gfxg f x=D169 Example: Let ( )5f xx=−and 2( )2g xx=−. Find: (a) ()(4)fg=D(b) ()(9)gf=D(c) Find the composite functions and their domains ()( )gfx=DDomain:
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