Pertanyaan

Diketahui f ( x ) = x + 3 54 dan g ( x ) = 2 x + 7 , tentukan ( f ∘ g ) ( x ) dan ( g ∘ f ) − 1 ( x )

Diketahui $f (x) = \frac{54}{x + 3}$ dan $g (x) = 2 x + 7$ , tentukan $(f \circ g) (x)$ dan $(g \circ f)^{- 1} (x)$

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N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Pembahasan

Fungsi komposisi didapatkan dengan mensubtitusikan fungsi ke dalam nilai Maka, Nilai : Maka,

Fungsi komposisi didapatkan dengan mensubtitusikan fungsi ke dalam nilai

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 54 over denominator x plus 3 end fraction end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 54 over denominator 2 x plus 7 plus 3 end fraction end cell row blank equals cell fraction numerator 54 over denominator 2 x plus 10 end fraction end cell end table$

Maka, $table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 54 over denominator 2 x plus 10 end fraction end cell end table$

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 2 open parentheses fraction numerator 54 over denominator x plus 3 end fraction close parentheses plus 7 end cell row blank equals cell fraction numerator 108 over denominator x plus 3 end fraction plus fraction numerator 7 x plus 21 over denominator x plus 3 end fraction end cell row blank equals cell fraction numerator 108 open parentheses 7 x plus 21 close parentheses over denominator x plus 3 end fraction end cell row y equals cell fraction numerator 756 x plus 2.268 over denominator x plus 3 end fraction end cell row cell y left parenthesis x plus 3 right parenthesis end cell equals cell 756 x plus 2.268 end cell row cell y x plus 3 y end cell equals cell 756 x plus 2.268 end cell row cell y x minus 756 x end cell equals cell 2.268 minus 3 y end cell row cell x left parenthesis y minus 756 right parenthesis end cell equals cell 2.268 minus 3 y end cell row x equals cell fraction numerator 2.268 minus 3 y over denominator y minus 756 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2.268 minus 3 x over denominator x minus 756 end fraction end cell end table$

Maka, $table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2.268 minus 3 x over denominator x minus 756 end fraction end cell end table$