Pertanyaan

1. Diketahui f ( x ) = 2 1 x − 1 dan g ( x ) = 2 x + 4 , t entukan : ( g ∘ f ) − 1 ( 10 ) = ...

1. Diketahui $f (x) = \frac{1}{2} x - 1 dan g (x) = 2 x + 4$ , tentukan :

$(g \circ f)^{- 1} (10) = ...$

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Pembahasan

Diketahui , Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell 1 half straight x minus 1 end cell row straight x equals cell 1 half straight y minus 1 end cell row cell straight x plus 1 end cell equals cell 1 half straight y end cell row cell 2 open parentheses straight x plus 1 close parentheses end cell equals straight y row cell 2 straight x plus 2 end cell equals straight y row cell straight f to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell 2 straight x plus 2 end cell row blank blank blank row cell straight g open parentheses straight x close parentheses end cell equals cell 2 straight x plus 4 end cell row straight x equals cell 2 straight y plus 4 end cell row cell straight x minus 4 end cell equals cell 2 straight y end cell row cell fraction numerator straight x minus 4 over denominator 2 end fraction end cell equals straight y row cell straight g to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator straight x minus 4 over denominator 2 end fraction end cell row blank blank blank row cell open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell straight f to the power of negative 1 end exponent open parentheses straight g to the power of negative 1 end exponent open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight f to the power of negative 1 end exponent open parentheses fraction numerator straight x minus 4 over denominator 2 end fraction close parentheses end cell row blank equals cell 2 open parentheses fraction numerator straight x minus 4 over denominator 2 end fraction close parentheses plus 2 end cell row blank equals cell fraction numerator 2 straight x minus 8 plus 4 over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 straight x minus 4 over denominator 2 end fraction end cell row blank equals cell straight x minus 2 end cell row cell open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses 10 close parentheses end cell equals cell 10 minus 2 end cell row blank equals 8 end table end style$

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