Previous
Next

2. Domini d'una funció

Domini d'una funció f és el conjunt de nombres reals on la funciío està definida. És a dir, que tenen imatge per f.

Ho podem designar per D(f),  Df,  dom(f)

El càlcul del domini d'una funció, depenent de com sigui aquesta funció, pot ser complicat.  Però en aquest bloc  ens limitarem a casos senzills:

        

Funcions polinòmiques

    El domini d'una funció polinòmica és tot straight real numbers (nombres reals)

    Exemples

    a right parenthesis space space f left parenthesis x right parenthesis equals x cubed minus 5 x squared plus 3 space space space space rightwards arrow space space space D subscript f equals straight real numbers

    b right parenthesis space space f left parenthesis x right parenthesis equals 2 left parenthesis x minus 1 right parenthesis cubed space space space space rightwards arrow space space space D subscript f equals straight real numbers

    c right parenthesis space space f left parenthesis x right parenthesis equals 1 half x cubed minus 5 x squared plus 2 over 3 space space space space rightwards arrow space space space D subscript f equals straight real numbers      

        

Funció racional

    Una funció racional és de la forma  f left parenthesis x right parenthesis equals fraction numerator P left parenthesis x right parenthesis over denominator Q left parenthesis x right parenthesis end fraction 

    El domini és tots els nombres excepte els que anul·len el denominador

    Exemples

     a right parenthesis space space f left parenthesis x right parenthesis equals 1 over x space space space rightwards arrow D subscript f equals straight real numbers minus open curly brackets 0 close curly brackets

     b right parenthesis space space f left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x plus 3 end fraction space space space rightwards arrow D subscript f equals straight real numbers minus open curly brackets negative 3 close curly brackets

     c right parenthesis space space f left parenthesis x right parenthesis equals fraction numerator x over denominator x squared minus 25 end fraction space space space rightwards arrow D subscript f equals straight real numbers minus open curly brackets plus-or-minus 5 close curly brackets

     d right parenthesis space space f left parenthesis x right parenthesis equals fraction numerator x squared over denominator x squared minus 3 x end fraction space space space rightwards arrow D subscript f equals straight real numbers minus open curly brackets 0 comma 3 close curly brackets

     e right parenthesis space space f left parenthesis x right parenthesis equals fraction numerator x over denominator x squared plus 1 end fraction space space space rightwards arrow D subscript f equals straight real numbers

     f)  f left parenthesis x right parenthesis equals fraction numerator x over denominator x squared minus x minus 2 end fraction space space space rightwards arrow D subscript f equals straight real numbers minus open curly brackets negative 1 comma 2 close curly brackets

                     

Funció irracional   

     Veiem alguns exemples

      a right parenthesis space space f left parenthesis x right parenthesis equals square root of x space space rightwards arrow space space space D subscript f equals left square bracket 0 comma plus infinity right parenthesis space space space     podríem posar també  D subscript f equals straight real numbers to the power of plus

      b right parenthesis space space f left parenthesis x right parenthesis equals square root of negative x end root space space rightwards arrow space space space D subscript f equals left parenthesis negative infinity comma 0 right square bracket space space space     podríem posar també  D subscript f equals straight real numbers to the power of minus

      c right parenthesis space space f left parenthesis x right parenthesis equals square root of x minus 1 end root space space rightwards arrow space space space D subscript f equals left square bracket 1 comma plus infinity right parenthesis space space space

      d right parenthesis space space f left parenthesis x right parenthesis equals square root of x squared plus 1 end root space space rightwards arrow space space space D subscript f equals straight real numbers

     d right parenthesis space space f left parenthesis x right parenthesis equals square root of x squared minus 1 end root space space rightwards arrow space space space D subscript f equals left parenthesis negative infinity comma negative 1 right square bracket union left square bracket 1 comma plus infinity right parenthesis equals straight real numbers minus left parenthesis negative 1 comma 1 right parenthesis

      d right parenthesis space space f left parenthesis x right parenthesis equals cube root of x space space rightwards arrow space space space D subscript f equals straight real numbers

      e right parenthesis space space f left parenthesis x right parenthesis equals cube root of x minus 1 end root space space rightwards arrow space space space D subscript f equals straight real numbers

Previous
Next