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Pertanyaan

Jika f ( x ) = x 2 + 3 x − 4 , g ( x ) = x − 4 , dan h ( x ) = 2 x + 1 , komposisi fungsi ( f ∘ g ∘ h ) ( x ) = ....

Jika , dan , komposisi fungsi  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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 open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals 4 x squared minus 6 x minus 4.

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Pembahasan

Diketahui , dan , maka: Sehingga: Jadi, .

Diketahui  f open parentheses x close parentheses equals x squared plus 3 x minus 4 comma space g open parentheses x close parentheses equals x minus 4, dan h open parentheses x close parentheses equals 2 x plus 1, maka:

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 open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses x minus 4 close parentheses open parentheses f ring operator g close parentheses open parentheses x close parentheses equals open parentheses x minus 4 close parentheses squared plus 3 open parentheses x minus 4 close parentheses minus 4 open parentheses f ring operator g close parentheses open parentheses x close parentheses equals x squared minus 8 x plus 16 plus 3 x minus 12 minus 4 open parentheses f ring operator g close parentheses open parentheses x close parentheses equals x squared minus 5 x 

Sehingga:

open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals open parentheses f ring operator g close parentheses open parentheses h open parentheses x close parentheses close parentheses open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals open parentheses f ring operator g close parentheses open parentheses 2 x plus 1 close parentheses open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals open parentheses 2 x plus 1 close parentheses squared minus 5 open parentheses 2 x plus 1 close parentheses open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals 4 x squared plus 4 x plus 1 minus 10 x minus 5 open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals 4 x squared minus 6 x minus 4 

Jadi, open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals 4 x squared minus 6 x minus 4.

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