Jika f(x)=2x dan g(x)=2x, tentukan 21​log(fog)(x).

Pertanyaan

Jika  dan , tentukan .

B. Hary

Master Teacher

Jawaban terverifikasi

Jawaban

 scriptbase log left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals negative 1 minus straight x end scriptbase presuperscript 1 half end presuperscript.

Pembahasan

Ingat konsep-konsep berikut!

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style

begin mathsize 14px style scriptbase log open parentheses b to the power of n close parentheses equals n over m scriptbase log open parentheses b close parentheses end scriptbase presuperscript a end scriptbase presuperscript a to the power of m end presuperscript end style 

begin mathsize 14px style scriptbase log open parentheses a close parentheses equals 1 end scriptbase presuperscript a end style 

Berdasarkan konsep tersebut diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 2 to the power of x close parentheses end cell row blank equals cell 2 open parentheses 2 to the power of x close parentheses end cell row blank equals cell 2 to the power of 1 plus x end exponent end cell end table end style  

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log open parentheses f ring operator g close parentheses open parentheses x close parentheses end scriptbase presuperscript 1 half end presuperscript end cell equals cell scriptbase log open parentheses 2 to the power of 1 plus x end exponent close parentheses end scriptbase presuperscript 2 to the power of negative 1 end exponent end presuperscript end cell row blank equals cell open parentheses fraction numerator 1 plus x over denominator negative 1 end fraction close parentheses times scriptbase log 2 space end scriptbase presuperscript 2 end cell row blank equals cell open parentheses negative 1 minus x close parentheses times 1 space end cell row blank equals cell negative 1 minus x space space end cell end table 

Dengan demikian, scriptbase log left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals negative 1 minus straight x end scriptbase presuperscript 1 half end presuperscript.

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