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Diketahui suatu fungsi  dan . Tentukan .

Diketahui suatu fungsi begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 4 over denominator x plus 3 end fraction end style dan begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 4 x plus 7 over denominator x minus 6 end fraction comma space x not equal to 6 end style. Tentukan begin mathsize 14px style f left parenthesis x right parenthesis end style.

  1. begin mathsize 14px style... end style 

  2. begin mathsize 14px style... end style 

Jawaban:

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis f open parentheses x close parentheses right parenthesis end cell row cell fraction numerator 4 x plus 7 over denominator x minus 6 end fraction end cell equals cell fraction numerator 4 over denominator f open parentheses x close parentheses plus 3 end fraction end cell row cell open parentheses 4 x plus 7 close parentheses open parentheses f open parentheses x close parentheses plus 3 close parentheses end cell equals cell 4 x minus 24 end cell row cell f left parenthesis x right parenthesis plus 3 end cell equals cell fraction numerator 4 x minus 24 over denominator 4 x plus 7 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 4 x minus 24 over denominator 4 x plus 7 end fraction minus 3 end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 24 over denominator 4 x plus 7 end fraction minus fraction numerator 3 open parentheses 4 x plus 7 close parentheses over denominator 4 x plus 7 end fraction end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 24 minus 12 x minus 21 over denominator 4 x plus 7 end fraction end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator negative 8 x minus 45 over denominator 4 x plus 7 end fraction end cell end table end style

Karena penyebut tidak boleh bernilai begin mathsize 14px style 0 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x plus 7 end cell not equal to 0 row cell 4 x end cell not equal to cell negative 7 end cell row x not equal to cell negative 7 over 4 end cell end table end style

Dengan demikian, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 8 x minus 45 over denominator 4 x plus 7 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table space 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 7 over 4 end cell end table end style.

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