Pertanyaan

Tentukan invers dari : a . f ( x ) = 3 x 2 + 6 x − 1

Tentukan invers dari :

$a . f (x) = 3 x^{2} + 6 x - 1$

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Habis dalam

Klaim

N. Putri

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Dari soal tersebut, dapat diperoleh invers fungsinya sebagai berikut:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 3 x squared plus 6 x minus 1 end cell row y equals cell 3 x squared plus 6 x minus 1 end cell row cell y over 3 end cell equals cell x squared plus 2 x minus 1 third end cell row cell x squared plus 2 x end cell equals cell y over 3 plus 1 third end cell row cell x squared plus 2 x plus 1 end cell equals cell y over 3 plus 1 third plus 1 end cell row cell open parentheses x plus 1 close parentheses squared end cell equals cell fraction numerator y plus 1 plus 3 over denominator 3 end fraction end cell row cell x plus 1 end cell equals cell square root of fraction numerator y plus 4 over denominator 3 end fraction end root end cell row x equals cell square root of fraction numerator y plus 4 over denominator 3 end fraction end root minus 1 end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell square root of fraction numerator x plus 4 over denominator 3 end fraction end root minus 1 end cell end table end style$