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

Pertanyaan

Jika $\style{font-size:14px}{f\left(x\right)=2x}$ dan $\style{font-size:14px}{g\left(x\right)=2^x}$ , tentukan $\style{font-size:14px}{{}^\frac12\log\left(fog\right)\left(x\right)}$ .

B. Hary

Master Teacher

Jawaban terverifikasi

Jawaban

${}^\frac12{\log{(\mathrm f\circ\mathrm g)}{(\mathrm x)}=-1-\mathrm x}$ .

Pembahasan

Ingat konsep-konsep berikut!

Berdasarkan konsep tersebut diperoleh

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, ${}^\frac12{\log{(\mathrm f\circ\mathrm g)}{(\mathrm x)}=-1-\mathrm x}$ .

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