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Diketahui f − 1 ( x ) = 5 x − 1 ​ dan g − 1 ( x ) = 2 3 − x ​ , nilai dari ( f ∘ g ) − 1 ( 2 ) = ....

Diketahui  dan , nilai dari  

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

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nilai dari adalah .

nilai dari open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses adalah 7 over 5.

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Pembahasan

Ingat kembali sifat invers fungsi komposisi: Diketahui dan . Maka: Jadi, nilai dari adalah .

Ingat kembali sifat invers fungsi komposisi:

open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals 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 

Diketahui f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 1 over denominator 5 end fraction dan straight g to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 3 minus straight x over denominator 2 end fraction. Maka:

open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals 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 open parentheses f ring operator g close parentheses to the power of negative 1 end exponent 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 f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals g to the power of negative 1 end exponent open parentheses fraction numerator x minus 1 over denominator 5 end fraction close parentheses open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 minus begin display style fraction numerator x minus 1 over denominator 5 end fraction end style over denominator 2 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator begin display style fraction numerator 15 minus x plus 1 over denominator 5 end fraction end style over denominator 2 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 16 minus x over denominator 5 end fraction times 1 half open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 16 minus x over denominator 10 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses equals fraction numerator 16 minus 2 over denominator 10 end fraction open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses equals 14 over 10 open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses equals 7 over 5  

Jadi, nilai dari open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses 2 close parentheses adalah 7 over 5.

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