Pertanyaan

Diketahui fungsi f − 1 ( x ) = x + 2 x , dan g − 1 ( x ) = 3 x 2 . Tentukan nilai dari ( f ∘ g ) ( 2 ) .

Diketahui fungsi $f^{- 1} (x) = \frac{x}{x + 2}$ , dan $g^{- 1} (x) = \frac{2}{3 x}$ . Tentukan nilai dari $(f \circ g) (2)$ .

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Klaim

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x over denominator x plus 2 end fraction end cell row y equals cell fraction numerator x over denominator x plus 2 end fraction end cell row cell y x plus 2 y end cell equals x row cell y x minus x end cell equals cell negative 2 y end cell row cell x left parenthesis y minus 1 right parenthesis end cell equals cell negative 2 y end cell row x equals cell fraction numerator negative 2 y over denominator y minus 1 end fraction end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator negative 2 x over denominator x minus 1 end fraction end cell row blank blank blank row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 2 over denominator 3 x end fraction end cell row y equals cell fraction numerator 2 over denominator 3 x end fraction end cell row cell 3 x end cell equals cell 2 over y end cell row x equals cell fraction numerator 2 over denominator 3 y end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 2 over denominator 3 x end fraction end cell row blank blank blank row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator negative 2 open parentheses begin display style fraction numerator 2 over denominator 3 x end fraction end style close parentheses over denominator begin display style fraction numerator 2 over denominator 3 x end fraction end style minus 1 end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator 4 over denominator 3 x end fraction end style over denominator begin display style fraction numerator 2 minus 3 x over denominator 3 x end fraction end style end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 2 minus 3 x end fraction end cell row blank blank blank row cell left parenthesis f ring operator g right parenthesis left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 4 over denominator 2 minus 3 left parenthesis 2 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 4 over denominator negative 4 end fraction end cell row blank equals 1 end table end style$