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Misalkan  begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 2 straight x plus 3 over denominator straight x minus 2 end fraction end style dan  begin mathsize 14px style straight g open parentheses straight x close parentheses equals square root of 5 straight x plus 3 end root end style,  tentukanlah :
 

begin mathsize 14px style left parenthesis straight g ring operator straight f right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end style    

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 straight x squared plus 9 over denominator straight x squared minus 13 end fraction end style 

Pembahasan

Diketahui:
begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 2 straight x plus 3 over denominator straight x minus 2 end fraction end style dan  begin mathsize 14px style straight g open parentheses straight x close parentheses equals square root of 5 straight x plus 3 end root end style

Ditanya : begin mathsize 14px style left parenthesis straight g ring operator straight f right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end style    = ....

Penyelesaian :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight f open parentheses straight x close parentheses close parentheses end cell row blank equals cell square root of 5 open parentheses straight f open parentheses straight x close parentheses close parentheses plus 3 end root end cell row blank equals cell square root of 5 open parentheses fraction numerator 2 straight x plus 3 over denominator straight x minus 2 end fraction close parentheses plus 3 end root end cell row blank equals cell square root of fraction numerator 10 straight x plus 15 over denominator straight x minus 2 end fraction plus fraction numerator 3 open parentheses straight x minus 2 close parentheses over denominator straight x minus 2 end fraction end root end cell row blank equals cell square root of fraction numerator 10 straight x plus 15 plus 3 straight x minus 6 over denominator straight x minus 2 end fraction end root end cell row blank equals cell square root of fraction numerator 13 straight x plus 9 over denominator straight x minus 2 end fraction end root end cell end table end style 
 

Selanjutnya, kita tentukan begin mathsize 14px style left parenthesis straight g ring operator straight f right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end style
 

begin mathsize 14px style misalkan space open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals straight y table attributes columnalign right center left columnspacing 2px end attributes row straight y equals cell square root of fraction numerator 13 straight x plus 9 over denominator straight x minus 2 end fraction end root end cell row cell straight y squared end cell equals cell fraction numerator 13 straight x plus 9 over denominator straight x minus 2 end fraction end cell row cell straight y squared open parentheses straight x minus 2 close parentheses end cell equals cell 13 straight x plus 9 end cell row cell xy squared minus 2 straight y squared end cell equals cell 13 straight x plus 9 end cell row cell xy squared minus 13 straight x end cell equals cell 2 straight y squared plus 9 end cell row cell straight x open parentheses straight y squared minus 13 close parentheses end cell equals cell 2 straight y squared plus 9 end cell row straight x equals cell fraction numerator 2 straight y squared plus 9 over denominator straight y squared minus 13 end fraction end cell row cell open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 2 straight x squared plus 9 over denominator straight x squared minus 13 end fraction end cell end table end style 
 

Jadi, begin mathsize 14px style open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 straight x squared plus 9 over denominator straight x squared minus 13 end fraction end style 

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