Roboguru

Diketahui , , dan , tentukan nilai

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals x end stylebegin mathsize 14px style g open parentheses x close parentheses equals 1 over x end style, dan begin mathsize 14px style h open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 3 end fraction end style, tentukan nilai begin mathsize 14px style f open parentheses x close parentheses times g open parentheses x squared minus 9 close parentheses minus h open parentheses x close parentheses end style

Jawaban:

Dengan menggunakan operasi perkalian dan pengurangan pada dua fungsi diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses times g open parentheses x squared minus 9 close parentheses minus h open parentheses x close parentheses end cell equals cell open parentheses x times open parentheses fraction numerator 1 over denominator x squared minus 9 end fraction close parentheses close parentheses minus fraction numerator 1 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator x over denominator x squared minus 9 end fraction minus fraction numerator 1 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator x over denominator x squared minus 9 end fraction minus fraction numerator x minus 3 over denominator open parentheses x plus 3 close parentheses open parentheses x minus 3 close parentheses end fraction end cell row blank equals cell fraction numerator x over denominator x squared minus 9 end fraction minus fraction numerator x minus 3 over denominator x squared minus 9 end fraction end cell row blank equals cell fraction numerator x minus open parentheses x minus 3 close parentheses over denominator x squared minus 9 end fraction end cell row blank equals cell fraction numerator 3 over denominator x squared minus 9 end fraction comma space x not equal to negative 3 comma space x not equal to 3 end cell row blank blank blank end table end style

Dengan demikian hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared minus 9 right parenthesis end cell 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 h end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 over denominator x squared minus 9 end fraction end cell 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 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 3 end table end style.

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