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Pertanyaan

Jika f ( x − 2 ) = 2 + 5 x 1 ​ , tentukan f − 1 ( x ) !

Jika , tentukan !

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G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

.

 f apostrophe left parenthesis x right parenthesis equals fraction numerator 1 minus 12 x over denominator 5 x end fraction.

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Pembahasan

Misal Masukan ke . Kemudian cari : Jadi, .

Misal

 table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals a row x equals cell a plus 2 end cell end table

Masukan x equals a plus 2 ke f left parenthesis x minus 2 right parenthesis equals fraction numerator 1 over denominator 2 plus 5 x end fraction.

f left parenthesis a right parenthesis equals fraction numerator 1 over denominator 2 plus 5 left parenthesis a plus 2 right parenthesis end fraction equals fraction numerator 1 over denominator 2 plus 5 a plus 10 end fraction equals fraction numerator 1 over denominator 5 a plus 12 end fraction

Kemudian cari f to the power of negative 1 end exponent left parenthesis x right parenthesis :

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator 5 x plus 12 end fraction end cell equals y row 1 equals cell y open parentheses 5 x plus 12 close parentheses end cell row 1 equals cell 5 x y plus 12 y end cell row cell 5 x y end cell equals cell 1 minus 12 y end cell row x equals cell fraction numerator 1 minus 12 y over denominator 5 y end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 1 minus 12 x over denominator 5 x end fraction end cell end table

Jadi, f apostrophe left parenthesis x right parenthesis equals fraction numerator 1 minus 12 x over denominator 5 x end fraction.

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