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Diketahui fungsi  dan  adalah invers fungsi . Nila...

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 9 x plus 17 over denominator x plus 2 end fraction comma space x not equal to 2 end style dan begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style adalah invers fungsi begin mathsize 14px style f open parentheses x close parentheses end style. Nilai  dari begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah ... 

  1. begin mathsize 14px style negative 16 end style 

  2. begin mathsize 14px style negative 3 end style 

  3. begin mathsize 14px style negative 2 end style 

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style 12 end style 

Jawaban:

Pertama akan dicari invers dari fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 9 x plus 17 over denominator x plus 2 end fraction comma space x not equal to 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 9 x plus 17 over denominator x plus 2 end fraction end cell row cell y x plus 2 y end cell equals cell 9 x plus 17 end cell row cell 9 x minus y x end cell equals cell 2 y minus 17 end cell row cell x open parentheses 9 minus y close parentheses end cell equals cell 2 y minus 17 end cell row x equals cell fraction numerator 2 y minus 17 over denominator 9 minus y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x minus 17 over denominator 9 minus x end fraction end cell end table end style     

Selanjutnya akan ditentukan  nilai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses 10 close parentheses end cell equals cell fraction numerator 2 open parentheses 10 close parentheses minus 17 over denominator 9 minus 10 end fraction end cell row blank equals cell fraction numerator 20 minus 17 over denominator negative 1 end fraction end cell row blank equals cell negative 3 end cell end table end style        

 Jadi,nilai fungsi begin mathsize 14px style f to the power of negative 1 end exponent open parentheses 10 close parentheses end style adalah begin mathsize 14px style negative 3 end style

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