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Perhatikan gambar grafik fungsi berikut!

Fungsi invers dari 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 left parenthesis x right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 minus x over denominator 2 end fraction end cell end table end style 

  2. begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x minus 9 over denominator 2 end fraction end cell end table end style 

  3.  begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 9 over denominator 2 end fraction end cell end table end style  

  4. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals x minus 1 end style 

  5. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals 1 plus x end style 

W. Sholihah

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Dapat diperhatikan bahwa grafiknya berupa garis lurus. Artinya, fungsi begin mathsize 14px style f open parentheses x close parentheses end style adalah fungsi linear sehingga bisa kita misalkan dengan begin mathsize 14px style f left parenthesis x right parenthesis equals a x plus b end style.

Kemudian, dari gambar grafik tersebut, kita ketahui bahwa grafik melalui titik begin mathsize 14px style left parenthesis 4 comma space 1 right parenthesis end style dan begin mathsize 14px style left parenthesis 2 comma space 5 right parenthesis end style.

Akibatnya, kita dapatkan bahwa begin mathsize 14px style f left parenthesis 4 right parenthesis equals 1 end style dan begin mathsize 14px style f left parenthesis 2 right parenthesis equals 5 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 4 right parenthesis end cell equals 1 row cell a left parenthesis 4 right parenthesis plus b end cell equals 1 row cell 4 a plus b end cell equals cell 1 space space space... space open parentheses 1 close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 2 close parentheses end cell equals 5 row cell a open parentheses 2 close parentheses plus b end cell equals 5 row cell 2 a plus b end cell equals cell 5 space space... left parenthesis 2 right parenthesis end cell end table end style 

Kita eliminasi nilai begin mathsize 14px style b end style dari persamaan (1) dan persamaan (2) sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell 4 a plus b equals 1 end cell row cell 2 a plus b equals 5 minus end cell row cell 2 a equals negative 4 end cell row cell a equals negative 2 end cell end table end cell end table end style 

Kemudian, kita substitusikan nilai begin mathsize 14px style a equals negative 2 end style ke salah satu persamaan. Kita pilih persamaan (1).

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a plus b end cell equals 1 row cell 4 left parenthesis negative 2 right parenthesis plus b end cell equals 1 row cell negative 8 plus b end cell equals 1 row b equals 9 end table end style

Oleh karena itu, begin mathsize 14px style f left parenthesis x right parenthesis equals negative a x plus b equals negative 2 x plus 9 end style.

Selanjutnya, kita cari fungsi inversnya.

Misal undefined, maka undefined.

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

Dengan demikian, fungsi invers dari begin mathsize 14px style f open parentheses x close parentheses end style adalah begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 minus x over denominator 2 end fraction end cell end table end style.

Jadi, jawaban yang tepat adalah A.

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