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Jika diketahui dan , nilai dari adalah ...

Jika diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 12 x squared minus 7 end style dan begin mathsize 14px style g open parentheses 1 over x close parentheses equals fraction numerator x minus 2 over denominator 4 x plus 1 end fraction end style, nilai dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses 2 close parentheses end style adalah ...

  1. undefined 

  2. begin mathsize 14px style 3 end style 

  3. begin mathsize 14px style negative 3 end style 

  4. undefined 

  5. begin mathsize 14px style negative 6 end style 

Jawaban:

Fungsi komposisi adalah gabungan dari beberapa fungsi yang ada.

Diketahui:

begin mathsize 14px style f left parenthesis x right parenthesis equals 12 x squared minus 7 end style
begin mathsize 14px style g open parentheses 1 over x close parentheses equals fraction numerator x minus 2 over denominator 4 x plus 1 end fraction end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 1 over x right parenthesis end cell equals cell fraction numerator x minus 2 over denominator 4 x plus 1 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator begin display style 1 over x minus 2 end style over denominator 4 left parenthesis begin display style 1 over x end style right parenthesis plus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 minus 2 x over denominator x end fraction end style over denominator begin display style 4 over x plus 1 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 minus 2 x over denominator x end fraction end style over denominator begin display style fraction numerator 4 plus x over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator 1 minus 2 x over denominator 4 plus x end fraction end cell end table end style 

Sehingga, begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses 2 close parentheses end style dapat dihitung dengan menentukan begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style terlebih dahulu.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 12 open parentheses fraction numerator 1 minus 2 x over denominator 4 plus x end fraction close parentheses squared minus 7 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis end cell equals cell 12 open parentheses fraction numerator 1 minus 2 left parenthesis 2 right parenthesis over denominator 4 plus 2 end fraction close parentheses squared minus 7 end cell row blank equals cell 12 open parentheses fraction numerator 1 minus 4 over denominator 6 end fraction close parentheses squared minus 7 end cell row blank equals cell 12 open parentheses fraction numerator negative 3 over denominator 6 end fraction close parentheses squared minus 7 end cell row blank equals cell 12 open parentheses negative 1 half close parentheses squared minus 7 end cell row blank equals cell 12 open parentheses 1 fourth close parentheses minus 7 end cell row blank equals cell 3 minus 7 end cell row blank equals cell negative 4 end cell end table end style

Maka,  nilai dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses 2 close parentheses end style adalah begin mathsize 14px style negative 4 end style

Jadi, jawaban yang tepat adalah D.

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