Pertanyaan

Salah satu rumus fungsi invers dari g ( x ) = 2 x 2 − 3 x + 1 adalah ...

Salah satu rumus fungsi invers dari $g (x) = 2 x^{2} - 3 x + 1$ adalah ...

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Klaim

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Diperoleh invers fungsi kuadrat yaitu: Maka,fungsi invers dari adalah .

Diperoleh invers fungsi kuadrat yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell 2 x squared minus 3 x plus 1 end cell row y equals cell 2 x squared minus 3 x plus 1 end cell row cell 2 x squared minus 3 x end cell equals cell y minus 1 end cell row cell fraction numerator 2 x squared minus 3 x over denominator 2 end fraction end cell equals cell fraction numerator y minus 1 over denominator 2 end fraction end cell row cell x squared minus 3 over 2 x end cell equals cell 1 half y minus 1 half end cell row cell x squared minus 3 over 2 x plus 9 over 16 end cell equals cell 1 half y minus 1 half plus 9 over 16 end cell row cell open parentheses x minus 3 over 4 close parentheses squared end cell equals cell 1 half y minus 8 over 16 plus 9 over 16 end cell row cell open parentheses x minus 3 over 4 close parentheses squared end cell equals cell 1 half y plus 1 over 16 end cell row cell x minus 3 over 4 end cell equals cell plus-or-minus square root of 1 half y plus 1 over 16 end root end cell row x equals cell 3 over 4 plus-or-minus square root of 1 half y plus 1 over 16 end root end cell row x equals cell 3 over 4 plus-or-minus square root of 8 over 16 y plus 1 over 16 end root end cell row x equals cell 3 over 4 plus-or-minus fraction numerator square root of 8 y plus 1 end root over denominator 4 end fraction end cell row x equals cell fraction numerator 3 plus-or-minus square root of 8 y plus 1 end root over denominator 4 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 3 plus-or-minus square root of 8 x plus 1 end root over denominator 4 end fraction end cell end table$

Maka, fungsi invers dari g open parentheses x close parentheses equals 2 x squared minus 3 x plus 1 adalah $g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 plus-or-minus square root of 8 x plus 1 end root over denominator 4 end fraction$ .