Pertanyaan

f ( x ) = x − 4 , g ( x ) = x − 5 11 x + 4 ​ , x  = 5 Tentukan ( f ∘ g ) ( x ) dan ( f ∘ g ) ( 3 )

Tentukan  dan 

 

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

dan .

 open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator 7 x plus 24 over denominator x minus 5 end fraction spacedan open parentheses f ring operator g close parentheses open parentheses 3 close parentheses equals negative 22 comma 5 .      

Pembahasan

Jadi, dan .

f open parentheses x close parentheses equals x minus 4 comma space g open parentheses x close parentheses equals fraction numerator 11 x plus 4 over denominator x minus 5 end fraction comma space x not equal to 5 open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses space space space space space space space space space space space space space equals f open parentheses fraction numerator 11 x plus 4 over denominator x minus 5 end fraction close parentheses space space space space space space space space space space space space space equals fraction numerator 11 x plus 4 over denominator x minus 5 end fraction minus 4 space space space space space space space space space space space space space equals fraction numerator open parentheses 11 x plus 4 close parentheses minus 4 open parentheses x minus 5 close parentheses over denominator x minus 5 end fraction space space space space space space space space space space space space space equals fraction numerator 7 x plus 24 over denominator x minus 5 end fraction space space space space space space space space space space space space space space space space space space space space space space rightwards arrow space space space space space space open parentheses f ring operator g close parentheses open parentheses 3 close parentheses equals fraction numerator 7 open parentheses 3 close parentheses plus 24 over denominator 3 minus 5 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 45 over denominator negative 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative 22 comma 5 space  

Jadi, open parentheses f ring operator g close parentheses open parentheses x close parentheses equals fraction numerator 7 x plus 24 over denominator x minus 5 end fraction spacedan open parentheses f ring operator g close parentheses open parentheses 3 close parentheses equals negative 22 comma 5 .      

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Diketahui fungsi f : R → R dan g : R → R dirumuskan dengan f ( x ) = x x − 1 ​ , untuk x  = 0 dan g ( x ) = x + 3 . Tentukanlah ( g ∘ f ( x ) ) − 1 .

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