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Pertanyaan

Jika f ( x ) = x x + 1 ​ dan g ( x ) = x − 2 , tentukan [ g ( f ( x ) ) ] − 1 !

Jika  dan , tentukan !

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

adalah .

 begin mathsize 14px style open square brackets g open parentheses f open parentheses x close parentheses close parentheses close square brackets to the power of negative 1 end exponent end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator x plus 1 end fraction end cell end table.

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Pembahasan

Diketahui: Ditanya: ? Jawab: Sekarang kita cari inversnya Jadi, adalah .

Diketahui:

  • begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator x end fraction end style
  • begin mathsize 14px style g left parenthesis x right parenthesis equals x minus 2 end style

Ditanya:

  • begin mathsize 14px style open square brackets g open parentheses f open parentheses x close parentheses close parentheses close square brackets to the power of negative 1 end exponent end style?

Jawab:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell g open parentheses fraction numerator x plus 1 over denominator x end fraction close parentheses end cell row blank equals cell fraction numerator x plus 1 over denominator x end fraction minus 2 end cell row blank equals cell fraction numerator x plus 1 over denominator x end fraction minus fraction numerator 2 x over denominator x end fraction end cell row blank equals cell fraction numerator 1 minus x over denominator x end fraction end cell end table end style 

Sekarang kita cari inversnya

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell fraction numerator 1 minus x over denominator x end fraction end cell row cell Misal space g open parentheses f open parentheses x close parentheses close parentheses end cell equals y row y equals cell fraction numerator 1 minus x over denominator x end fraction end cell row cell y x end cell equals cell 1 minus x end cell row cell y x plus x end cell equals 1 row cell x open parentheses y plus 1 close parentheses end cell equals 1 row x equals cell fraction numerator 1 over denominator y plus 1 end fraction end cell row cell open square brackets g open parentheses f open parentheses x close parentheses close parentheses close square brackets to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator x plus 1 end fraction end cell end table  

Jadi, begin mathsize 14px style open square brackets g open parentheses f open parentheses x close parentheses close parentheses close square brackets to the power of negative 1 end exponent end style adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator x plus 1 end fraction end cell end table.

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