Pertanyaan

2. Diketahui f ( x ) = 2 x − 1 dan g ( x ) = 3 x + 5 . Tentukan : c. ( g ∘ f ) − 1 ( x ) = ....

2. Diketahui $f (x) = 2 x - 1 dan g (x) = 3 x + 5$ .

Tentukan :

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

R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

Jawaban terverifikasi

Pembahasan

Diketahui . Ditanya : tentukan Dijawab :

Diketahui .

Ditanya : tentukan

Dijawab :

$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 2 straight x minus 1 end cell row straight x equals cell 2 straight y minus 1 end cell row cell straight x plus 1 end cell equals cell 2 straight y end cell row cell fraction numerator straight x plus 1 over denominator 2 end fraction 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 fraction numerator straight x plus 1 over denominator 2 end fraction end cell row blank blank blank row cell straight g open parentheses straight x close parentheses end cell equals cell 3 straight x plus 5 end cell row straight x equals cell 3 straight y plus 5 end cell row cell straight x minus 5 end cell equals cell 3 straight y end cell row cell fraction numerator straight x minus 5 over denominator 3 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 5 over denominator 3 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 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 fraction numerator straight x minus 5 over denominator 3 end fraction close parentheses end cell 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 fraction numerator open parentheses fraction numerator straight x minus 5 over denominator 3 end fraction close parentheses plus 1 over denominator 2 end fraction end cell 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 fraction numerator begin display style fraction numerator straight x minus 5 plus 3 over denominator 3 end fraction end style over denominator 2 end fraction end cell 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 fraction numerator straight x minus 2 over denominator 6 end fraction end cell end table end style$