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Misalkan  f(x)=x−22x+3​ dan  g(x)=5x+3​,  tentukanlah :   ((f∘g)−1)−1(x)

Pertanyaan

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 :
 

undefined     

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 square root of 5 straight x plus 3 end root plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 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 : undefined   = ....

Penyelesaian :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end cell row blank equals cell straight f left parenthesis straight g open parentheses straight x close parentheses right parenthesis end cell row blank equals cell fraction numerator 2 open parentheses straight g open parentheses straight x close parentheses close parentheses plus 3 over denominator straight g open parentheses straight x close parentheses minus 2 end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 5 straight x plus 3 end root close parentheses plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 end fraction end cell end table end style 

Jadi, begin mathsize 14px style open parentheses open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 2 square root of 5 straight x plus 3 end root plus 3 over denominator square root of 5 straight x plus 3 end root minus 2 end fraction end style 

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Jika f−1(x)=2x−1​, g(x)=5x2+3, dan h−1(x)=7x​, maka (f∘g∘h)=...

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