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Diketahui f(x)=2x+94x−5​, x=−29​ dan f−1(x) adalah invers dari f(x), maka rumus  adalah ...

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fractionx not equal to negative 9 over 2 dan f to the power of negative 1 end exponent left parenthesis x right parenthesis adalah invers dari f left parenthesis x right parenthesis, maka rumus f to the power of negative 1 end exponent left parenthesis x right parenthesis adalah ...

  1. fraction numerator 9 x minus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2

  2. fraction numerator 5 minus 9 x over denominator 2 x minus 4 end fraction comma space x not equal to 2

  3. fraction numerator negative 9 x minus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2

  4. fraction numerator negative 9 x minus 5 over denominator 2 x plus 4 end fraction comma space x not equal to negative 2

  5. fraction numerator negative 9 x plus 5 over denominator 2 x plus 4 end fraction comma space x not equal to negative 2

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Untuk melakukan invers, pertama kita misalkan y equals f left parenthesis x right parenthesis.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction end cell row cell y times open parentheses 2 x plus 9 close parentheses end cell equals cell 4 x minus 5 end cell row cell 2 x y plus 9 y end cell equals cell 4 x minus 5 end cell row cell 2 x y minus 4 x end cell equals cell negative 9 y minus 5 end cell row cell x times open parentheses 2 y minus 4 close parentheses end cell equals cell negative 9 y minus 5 end cell row x equals cell fraction numerator negative 9 y minus 5 over denominator 2 y minus 4 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 negative 9 y minus 5 over denominator 2 y minus 4 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 negative 9 x minus 5 over denominator 2 x minus 4 end fraction end cell end table


Karena f to the power of negative 1 end exponent left parenthesis x right parenthesis berupa fungsi rasional, maka ada domain khusus, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 4 end cell not equal to 0 row cell 2 x end cell not equal to 4 row x not equal to 2 end table

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 9 x minus 5 over denominator 2 x minus 4 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank not equal to blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table.

Oleh karena itu, jawaban yang benar adalah C.

41

4.2 (4 rating)

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