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Pertanyaan

2. Fungsi f : R → R dan g : R → R didefinisikan oleh f ( x ) = 2 x + 11 dan g ( x ) = 1 − x . Tentukan: c. ( g ∘ f − 1 ) ( x )

2. Fungsi  didefinisikan oleh  dan . Tentukan:

c.    

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R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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.

 open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator 13 minus x over denominator 2 end fraction .space 

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Pembahasan

Perhatikan penghitungan berikut! sehingga, yaitu: Jadi, .

Perhatikan penghitungan berikut!

 f open parentheses x close parentheses equals 2 x plus 11 misal colon space y equals f open parentheses x close parentheses space maka space x equals f to the power of negative 1 end exponent open parentheses x close parentheses f open parentheses x close parentheses equals 2 x plus 11 y equals 2 x plus 11 y minus 11 equals 2 x fraction numerator y minus 11 over denominator 2 end fraction equals x f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 11 over denominator 2 end fraction  g open parentheses x close parentheses equals 1 minus x misal colon space z equals g open parentheses x close parentheses space maka space x equals g to the power of negative 1 end exponent open parentheses x close parentheses g open parentheses x close parentheses equals 1 minus x z equals 1 minus x x equals 1 minus z g to the power of negative 1 end exponent open parentheses x close parentheses equals 1 minus x  

sehingga, open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses yaitu:

 open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals g open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals g open parentheses fraction numerator x minus 11 over denominator 2 end fraction close parentheses open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals 1 minus open parentheses fraction numerator x minus 11 over denominator 2 end fraction close parentheses open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals 2 over 2 minus open parentheses fraction numerator x minus 11 over denominator 2 end fraction close parentheses open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator 2 minus x plus 11 over denominator 2 end fraction open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator 13 minus x over denominator 2 end fraction             

Jadi, open parentheses g ring operator f to the power of negative 1 end exponent close parentheses open parentheses x close parentheses equals fraction numerator 13 minus x over denominator 2 end fraction .space 

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