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Jika f(x)=x1​ dan g(x)=2x−1, tentukan (f∘g)−1(x).

Pertanyaan

Jika  dan , tentukan .  

  1. ... 

  2. ... 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style bold left parenthesis bold f bold ring operator bold g bold right parenthesis to the power of bold minus bold 1 end exponent begin bold style left parenthesis x right parenthesis end style bold equals fraction numerator bold x bold plus bold 1 over denominator bold 2 bold x end fraction end style 

Pembahasan

Ingat!

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 artinya begin mathsize 14px style g end style dimasukkan ke begin mathsize 14px style f end style 

begin mathsize 14px style y equals h open parentheses x close parentheses space left right arrow x equals h to the power of negative 1 end exponent open parentheses y close parentheses 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 x minus 1 close parentheses end cell row blank equals cell fraction numerator 1 over denominator 2 x minus 1 end fraction end cell end table end style  

Akan dicari invers dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 1 over denominator 2 x minus 1 end fraction end cell row cell 2 x minus 1 end cell equals cell 1 over y end cell row cell 2 x end cell equals cell 1 over y plus 1 end cell row x equals cell fraction numerator 1 over denominator 2 y end fraction plus 1 half end cell row x equals cell fraction numerator 1 over denominator 2 y end fraction plus fraction numerator y over denominator 2 y end fraction end cell row x equals cell fraction numerator 1 plus y over denominator 2 y end fraction end cell row x equals cell fraction numerator y plus 1 over denominator 2 y end fraction end cell end table end style 

Dengan demikian begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator y plus 1 over denominator 2 y end fraction end style, atau begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 x end fraction end style  

Jadi, begin mathsize 14px style bold left parenthesis bold f bold ring operator bold g bold right parenthesis to the power of bold minus bold 1 end exponent begin bold style left parenthesis x right parenthesis end style bold equals fraction numerator bold x bold plus bold 1 over denominator bold 2 bold x end fraction end style 

100

4.6 (5 rating)

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