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Diberikan begin mathsize 14px style f open parentheses fraction numerator x plus 5 over denominator x minus 6 end fraction close parentheses equals x end style untuk begin mathsize 14px style x not equal to 6 end style dan begin mathsize 14px style x not equal to 1 end style. Tentukan begin mathsize 14px style f open parentheses 2 x close parentheses end style.

Jawaban:

Dengan meruntun dari cara memperoleh nilai suatu fungsi maka diperolah penjabaran sebagai berikut:

begin mathsize 14px style f open parentheses fraction numerator x plus 5 over denominator x minus 6 end fraction close parentheses equals x end style , begin mathsize 14px style x not equal to 6 end style , begin mathsize 14px style x not equal to 1 end style

Buat pemisalan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 5 over denominator x minus 6 end fraction end cell equals a row cell x minus 5 end cell equals cell a open parentheses x minus 6 close parentheses end cell row cell x minus 5 end cell equals cell a x minus 6 a end cell row cell x minus a x end cell equals cell 5 minus 6 a end cell row cell x open parentheses 1 minus a close parentheses end cell equals cell 5 minus 6 a end cell row x equals cell fraction numerator 5 minus 6 a over denominator 1 minus a end fraction end cell row blank blank blank end table end style

Selanjutnya subtitusikan begin mathsize 14px style x end style dan begin mathsize 14px style a end style pada nilai fungsi yang diketahui

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses fraction numerator x plus 5 over denominator x minus 6 end fraction close parentheses end cell equals x row cell f open parentheses a close parentheses end cell equals cell fraction numerator 6 a plus 5 over denominator a minus 1 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 6 x plus 5 over denominator x minus 1 end fraction end cell row cell f open parentheses 2 x close parentheses end cell equals cell fraction numerator 6 open parentheses 2 x close parentheses plus 5 over denominator 2 x minus 1 end fraction end cell row cell f open parentheses 2 x close parentheses end cell equals cell fraction numerator 12 x plus 5 over denominator 2 x minus 1 end fraction space comma space x not equal to 1 half end cell end table end style

Dengan demikian hasil dari begin mathsize 14px style f open parentheses 2 x close parentheses end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 12 x plus 5 over denominator 2 x minus 1 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table end style.

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