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Jika diketahui fungsi . Invers fungsi  adalah ...

Pertanyaan

Jika diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x minus 6 over denominator 3 x minus 2 end fraction comma space x not equal to 3 over 2 end style. Invers fungsi begin mathsize 14px style f open parentheses x close parentheses end style adalah ... 

  1. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 x minus 6 over denominator 3 x minus 5 end fraction comma space x not equal to 5 over 3 end style  

  2. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 x plus 6 over denominator 3 x plus 5 end fraction comma space x not equal to negative 5 over 3 end style   

  3. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 2 x plus 6 over denominator 3 x minus 5 end fraction comma space x not equal to 5 over 3 end style   

  4. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x minus 5 over denominator 2 x minus 6 end fraction comma space x not equal to 3 end style 

  5. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x minus 6 over denominator 2 x minus 5 end fraction comma space x not equal to 5 over 2 end style 

Pembahasan Soal:

Akan dicari invers dari fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x minus 6 over denominator 3 x minus 2 end fraction comma space x not equal to 3 over 2 end style dengan cara berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 5 x minus 6 over denominator 3 x minus 2 end fraction end cell row cell 3 y x minus 2 y end cell equals cell 5 x minus 6 end cell row cell 3 y x minus 5 x end cell equals cell 2 y minus 6 end cell row cell x open parentheses 3 y minus 5 close parentheses end cell equals cell 2 y minus 6 end cell row x equals cell fraction numerator 2 y minus 6 over denominator 3 y minus 5 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 6 over denominator 3 x minus 5 end fraction comma space x equals 5 over 3 end cell row blank blank blank end table end style      

Jadi, jawaban yang tepat adalah 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 11 April 2021

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