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

Pertanyaan

2. Fungsi f colon space straight real numbers rightwards arrow straight real numbers space dan space g colon space straight real numbers rightwards arrow straight real numbers didefinisikan oleh f open parentheses x close parentheses equals 2 x plus 11 dan g open parentheses x close parentheses equals 1 minus x. Tentukan:

h. 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 x close parentheses         

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

 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 x close parentheses equals fraction numerator 13 minus x over denominator 2 end fraction .space 

Pembahasan

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

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