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Pertanyaan

Bila f(x) memenuhi 2 f ( x ) + f ( 1 − x ) = x 2 untuk semua nilai real x, maka f(x) sama dengan.…

Bila f(x) memenuhi untuk semua nilai real x, maka f(x) sama dengan.…

  1. 1 half x squared minus 3 over 2 x plus 1 half

  2. 1 over 9 x squared plus 8 over 9 x minus 1 third

  3. 2 over 3 x squared plus 1 half x minus 1 third

  4. 1 third x squared plus 2 over 3 x minus 1 third

  5. 1 over 9 x squared plus x minus 4 over 9

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

.

 f open parentheses x close parentheses equals 1 third x squared plus 2 over 3 x minus 1 third.

Pembahasan

Substitusikan x = a Subtitusikan x = 1 – a Sehingga .

2 f left parenthesis x right parenthesis plus f left parenthesis 1 minus x right parenthesis equals x squared

Substitusikan x = a

2 f left parenthesis a right parenthesis plus f left parenthesis 1 minus a right parenthesis equals a squared

Subtitusikan x = 1 – a

2 f left parenthesis 1 minus a right parenthesis plus f left parenthesis 1 minus left parenthesis 1 minus a right parenthesis right parenthesis equals left parenthesis 1 minus a right parenthesis squared 2 f left parenthesis 1 minus a right parenthesis plus f left parenthesis a right parenthesis equals left parenthesis 1 minus a right parenthesis squared table row cell 2 f left parenthesis a right parenthesis plus f left parenthesis 1 minus a right parenthesis equals a squared end cell row cell f left parenthesis a right parenthesis plus 2 f left parenthesis 1 minus a right parenthesis equals left parenthesis 1 minus a right parenthesis squared end cell end table open parentheses table row cell cross times 2 end cell row cell cross times 1 end cell end table close parentheses  table row cell 4 f left parenthesis a right parenthesis plus 2 f left parenthesis 1 minus a right parenthesis equals 2 a squared end cell row cell bottom enclose f left parenthesis a right parenthesis plus 2 f left parenthesis 1 minus a right parenthesis equals left parenthesis 1 minus a right parenthesis squared end enclose end cell end table subscript minus 3 f left parenthesis a right parenthesis equals 2 a squared minus left parenthesis 1 minus a right parenthesis squared 3 f left parenthesis a right parenthesis equals 2 a squared minus left parenthesis a squared minus 2 a plus 1 right parenthesis 3 f left parenthesis a right parenthesis equals a squared plus 2 a minus 1 f open parentheses a close parentheses equals 1 third a squared plus 2 over 3 a minus 1 third

 Sehingga f open parentheses x close parentheses equals 1 third x squared plus 2 over 3 x minus 1 third.

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