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JIka diketahui  dan , nilai dari  adalah ...

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

  1. -3 

  2. -4 

  3. -6 

Jawaban:

diketahui begin mathsize 14px style straight f open parentheses straight x close parentheses equals 12 straight x squared minus 7 end style

diketahui begin mathsize 14px style straight g open parentheses 1 over straight x close parentheses equals fraction numerator straight x minus 2 over denominator 4 straight x plus 1 end fraction end style, maka begin mathsize 14px style straight g open parentheses straight x close parentheses space equals end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row misal colon blank row cell 1 over straight x end cell equals straight a row straight x equals cell 1 over straight a end cell row cell straight g open parentheses straight a close parentheses end cell equals cell straight g open parentheses straight x close parentheses end cell row cell straight g open parentheses 1 over straight x close parentheses end cell equals cell fraction numerator straight x minus 2 over denominator 4 straight x plus 1 end fraction end cell row cell straight g open parentheses straight x close parentheses end cell equals cell fraction numerator begin display style 1 over straight x end style minus 2 over denominator 4 open parentheses begin display style 1 over straight x end style close parentheses plus 1 end fraction end cell row cell straight g open parentheses straight x close parentheses end cell equals cell fraction numerator begin display style fraction numerator 1 minus 2 straight x over denominator up diagonal strike straight x end fraction end style over denominator begin display style fraction numerator 4 straight x plus straight x over denominator up diagonal strike straight x end fraction end style end fraction end cell row cell straight g open parentheses straight x close parentheses end cell equals cell fraction numerator 1 minus 2 straight x over denominator 4 plus straight x end fraction end cell end table end style      
 

komposisi fungsi dari begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end cell equals cell 12 open parentheses fraction numerator 1 minus 2 straight x over denominator 4 plus straight x end fraction close parentheses squared minus 7 end cell row blank equals cell 12 open parentheses fraction numerator 1 minus 4 straight x plus 4 straight x squared over denominator 16 plus 8 straight x plus straight x squared end fraction close parentheses minus 7 end cell end table end style    
 

komposisi fungsi dari undefined 
 

table attributes columnalign right center left columnspacing 2px end attributes row cell begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis 2 right parenthesis end style end cell size 14px equals cell size 14px 12 begin mathsize 14px style left parenthesis fraction numerator 1 minus 4 open parentheses 2 close parentheses plus 4 open parentheses 2 close parentheses squared over denominator 16 plus 8 open parentheses 2 close parentheses plus open parentheses 2 close parentheses squared end fraction right parenthesis end style size 14px minus size 14px 7 end cell row blank size 14px equals cell size 14px 12 begin mathsize 14px style left parenthesis fraction numerator 1 minus 8 plus 16 over denominator 16 plus 16 plus 4 end fraction right parenthesis end style size 14px minus size 14px 7 end cell row blank size 14px equals cell size 14px 12 begin mathsize 14px style left parenthesis 9 over 36 right parenthesis end style size 14px minus size 14px 7 end cell row blank size 14px equals cell size 14px 3 size 14px minus size 14px 7 end cell row blank size 14px equals cell size 14px minus size 14px 4 end cell end table  
 

Jadi, begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses 2 close parentheses equals negative 4 end style  

Jadi, jawaban yang benar adalah D

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