Pertanyaan

Diketahui fungsi f ( x ) = 3 + 2 x , g ( x ) = x + 4 3 x − 1 , x  = − 4 . Invers dari ( f ∘ g ) ( x ) = ...

Diketahui fungsi $f (x) = 3 + 2 x$ , $g (x) = \frac{3 x - 1}{x + 4}, x \neq = - 4$ . Invers dari $(f \circ g) (x) =$ ...

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Klaim

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Tentukan terlebih dahulu komposisi fungsi , yaitu: Kemudian tentukan invers dari . Maka, invers dari .

Tentukan terlebih dahulu komposisi fungsi open parentheses f ring operator g close parentheses open parentheses x close parentheses , yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator 3 x minus 1 over denominator x plus 4 end fraction close parentheses end cell row blank equals cell 3 plus 2 open parentheses fraction numerator 3 x minus 1 over denominator x plus 4 end fraction close parentheses end cell row blank equals cell 3 plus fraction numerator 6 x minus 2 over denominator x plus 4 end fraction end cell row blank equals cell fraction numerator 3 open parentheses x plus 4 close parentheses over denominator x plus 4 end fraction plus fraction numerator 6 x minus 2 over denominator x plus 4 end fraction end cell row blank equals cell fraction numerator 3 x plus 12 over denominator x plus 4 end fraction plus fraction numerator 6 x minus 2 over denominator x plus 4 end fraction end cell row blank equals cell fraction numerator 9 x plus 10 over denominator x plus 4 end fraction end cell end table$

Kemudian tentukan invers dari open parentheses f ring operator g close parentheses open parentheses x close parentheses .

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 9 x plus 10 over denominator x plus 4 end fraction end cell row y equals cell fraction numerator 9 x plus 10 over denominator x plus 4 end fraction end cell row cell y open parentheses x plus 4 close parentheses end cell equals cell 9 x plus 10 end cell row cell x y plus 4 y end cell equals cell 9 x plus 10 end cell row cell x y minus 9 x end cell equals cell negative 4 y plus 10 end cell row cell x open parentheses y minus 9 close parentheses end cell equals cell negative 4 y plus 10 end cell row x equals cell fraction numerator negative 4 y plus 10 over denominator y minus 9 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator negative 4 x plus 10 over denominator x minus 9 end fraction end cell end table$

Maka, invers dari $open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator negative 4 x plus 10 over denominator x minus 9 end fraction$ .