Roboguru

Jika  dan , maka tentukanlah nilai .

Pertanyaan

Jika begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 1 over denominator 5 end fraction end style dan begin mathsize 14px style g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 minus x over denominator 2 end fraction end style, maka tentukanlah nilai 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 end style.

Pembahasan Soal:

Diingat salah satu sifat dari invers fungsi kompoposisi yaitu

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 open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end style 

Diketahui  begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 1 over denominator 5 end fraction end style dan begin mathsize 14px style g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 minus x over denominator 2 end fraction end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell row blank equals cell g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell row blank equals cell g to the power of negative 1 end exponent open parentheses fraction numerator x minus 1 over denominator 5 end fraction close parentheses end cell row blank equals cell fraction numerator 3 minus begin display style fraction numerator x minus 1 over denominator 5 end fraction end style over denominator 2 end fraction end cell row blank equals cell 1 half times fraction numerator 15 minus x plus 1 over denominator 5 end fraction end cell row blank equals cell fraction numerator 16 minus x over denominator 10 end fraction end cell end table end style 

Dengan demikian diperoleh 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 16 minus x over denominator 10 end fraction end style.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 01 April 2021

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