Pertanyaan

Fungsi f : R → R , g : R → R ditentukan dengan rumus f ( x ) = x + 3 , g ( x ) = − 4 x , dan h ( x ) = 5 x + 1. Tentukan. 4. ( h − 1 ∘ f − 1 ∘ g − 1 ) ( x )

Fungsi $f : R \to R,$ $g : R \to R$ ditentukan dengan rumus $f (x) = x + 3,$ $g (x) = - 4 x,$ dan $h (x) = 5 x + 1.$

Tentukan.

4. $(h^{- 1} \circ f^{- 1} \circ g^{- 1}) (x)$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Fungsi

Fungsi $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight h to the power of negative 1 end exponent ring operator straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent right parenthesis left parenthesis straight x right parenthesis end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x plus 16 over denominator negative 20 end fraction end cell end table end style$

Pembahasan

Dengan menerapkan konsep invers fungsi komposisi: Dengan: Misalkan maka: Jadi, Fungsi

Dengan menerapkan konsep invers fungsi komposisi:

Dengan:

Misalkan begin mathsize 14px style straight y equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell end table end style maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell negative 20 straight x minus 16 end cell row cell straight y plus 16 end cell equals cell negative 20 straight x end cell row cell fraction numerator straight y plus 16 over denominator negative 20 end fraction end cell equals straight x row cell fraction numerator straight y plus 16 over denominator negative 20 end fraction end cell equals cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell row cell fraction numerator straight x plus 16 over denominator negative 20 end fraction end cell equals cell left parenthesis straight g ring operator straight f ring operator straight h right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell row cell fraction numerator straight x plus 16 over denominator negative 20 end fraction end cell equals cell left parenthesis straight h to the power of negative 1 end exponent ring operator straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent right parenthesis left parenthesis straight x right parenthesis end cell end table end style$

Jadi, Fungsi $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight h to the power of negative 1 end exponent ring operator straight f to the power of negative 1 end exponent ring operator straight g to the power of negative 1 end exponent right parenthesis left parenthesis straight x right parenthesis end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator straight x plus 16 over denominator negative 20 end fraction end cell end table end style$

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