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Pertanyaan

Jika begin mathsize 14px style f open parentheses x close parentheses equals 5 x plus 2 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 2 over 3 x minus 2 end style, maka begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals end style ...

  1. begin mathsize 14px style fraction numerator 2 x plus 3 over denominator 10 end fraction end style 

  2. begin mathsize 14px style fraction numerator 2 x minus 3 over denominator 10 end fraction end style 

  3. begin mathsize 14px style fraction numerator 3 x plus 2 over denominator 10 end fraction end style 

  4. begin mathsize 14px style fraction numerator 3 x plus 2 over denominator negative 10 end fraction end style 

  5. begin mathsize 14px style fraction numerator 3 x minus 2 over denominator 10 end fraction end style 

Pembahasan Soal:

Diketahui:

Fungsi begin mathsize 14px style f open parentheses x close parentheses equals 5 x plus 2 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 2 over 3 x minus 2 end style.

Tentukan terlebih dahulu fungsi komposisi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses end style seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell 2 over 3 open parentheses 5 x plus 2 close parentheses minus 2 end cell row blank equals cell 10 over 3 x plus 4 over 3 minus 2 end cell row blank equals cell 10 over 3 x plus 4 over 3 minus 6 over 3 end cell row blank equals cell 10 over 3 x minus 2 over 3 end cell end table end style

Kemudian tentukan nilai invers dari fungsi komposisi tersebut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 10 over 3 x minus 2 over 3 end cell row y equals cell fraction numerator 10 x minus 2 over denominator 3 end fraction end cell row cell 3 y end cell equals cell 10 x minus 2 end cell row cell 10 x end cell equals cell 3 y plus 2 end cell row x equals cell fraction numerator 3 y plus 2 over denominator 10 end fraction end cell row blank blank blank end table end style

Substitusi begin mathsize 14px style y equals x end style dan begin mathsize 14px style x equals y end style seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator 3 y plus 2 over denominator 10 end fraction end cell row y equals cell fraction numerator 3 x plus 2 over denominator 10 end fraction end cell end table end style

Maka, begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x plus 2 over denominator 10 end fraction end style.

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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