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Pertanyaan

Jika f ( x ) = 2 1 ​ x + 4 dan g ( x ) = 3 x − 7 , hitunglah ( g − 1 ∘ f − 1 ) ( − 2 ) − ( f − 1 ∘ g − 1 ) ( − 2 ) .

Jika , hitunglah 

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

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 begin mathsize 14px style left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis minus left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis equals 3 end style

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Pembahasan

, maka Jadi , berdasarkan sifat invers fungsi komposisi dapat ditulis . Jadi , berdasarkan sifat invers fungsi komposisi maka dapat ditulis . Maka Jadi .

begin mathsize 14px style f open parentheses x close parentheses equals 1 half x plus 4 space dan space g open parentheses x close parentheses equals 3 x minus 7 end style, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g open parentheses x close parentheses right parenthesis end cell row blank equals cell f left parenthesis 3 x minus 7 right parenthesis end cell row blank equals cell 1 half left parenthesis 3 x minus 7 right parenthesis plus 4 end cell row blank equals cell fraction numerator 3 x over denominator 2 end fraction minus 7 over 2 plus 4 end cell row blank equals cell fraction numerator 3 x minus 7 plus 8 over denominator 2 end fraction end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell row cell Jika space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 2 comma space maka space end cell row cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell equals cell negative 2 end cell row cell 3 x plus 1 end cell equals cell negative 4 end cell row cell 3 x end cell equals cell negative 5 end cell row x equals cell negative 5 over 3 end cell end table end style  

Jadi begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses equals negative 5 over 3 end style, berdasarkan sifat invers fungsi komposisi dapat ditulis begin mathsize 14px style open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses open parentheses negative 2 close parentheses equals negative 5 over 3 end style.  

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 g open parentheses 1 half x plus 4 close parentheses end cell row blank equals cell 3 open parentheses 1 half x plus 4 close parentheses minus 7 end cell row blank equals cell 3 over 2 x plus 12 minus 7 end cell row blank equals cell 3 over 2 x plus 5 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 10 over denominator 2 end fraction end cell row cell Jika space open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell negative 2 comma space maka space end cell row cell fraction numerator 3 x plus 10 over denominator 2 end fraction end cell equals cell negative 2 end cell row cell 3 x plus 10 end cell equals cell negative 4 end cell row cell 3 x end cell equals cell negative 14 end cell row x equals cell negative 14 over 3 end cell end table end style 

Jadi begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 2 close parentheses equals negative 14 over 3 end style, berdasarkan sifat invers fungsi komposisi maka dapat ditulis begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses negative 2 close parentheses equals negative 14 over 3 end style. Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis minus left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis end cell equals cell negative 5 over 3 minus open parentheses negative 14 over 3 close parentheses end cell row blank equals cell negative 5 over 3 plus 14 over 3 end cell row blank equals cell 9 over 3 end cell row blank equals 3 end table end style 

Jadi begin mathsize 14px style left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis minus left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis negative 2 right parenthesis equals 3 end style

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Jika f ( x ) = 3 x + 5 dan g ( x ) = 2 x + 3 x − 2 ​ , x  = − 2 3 ​ , hitunglah ( f ∘ g ) − 1 ( 6 ) + ( g ∘ f ) − 1 ( − 1 ) .

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