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Jika f ( x ) = 4 x , g ( x ) = x − 1 , dan h ( x ) = x 2 , tentukan ekspresi dari ( f ∘ g ∘ h ) ( x ) − ( h ∘ f ∘ g ) ( x ) + ( g ∘ h ∘ f ) ( x ) .

Jika , tentukan ekspresi dari . 

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L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

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Jawaban

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 begin mathsize 14px style left parenthesis f ring operator g ring operator h right parenthesis left parenthesis x right parenthesis minus left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis plus left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis equals 4 x squared plus 32 x minus 21 end style. 

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Pembahasan

Diketahui Menentukan Menentukan Menentukan Maka Jadi .

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 4 x comma space g open parentheses x close parentheses equals x minus 1 comma space dan space h open parentheses x close parentheses equals x squared end style 

Menentukan begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h close parentheses open parentheses x close parentheses end cell equals cell g open parentheses h open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x squared close parentheses end cell row blank equals cell x squared minus 1 end cell row blank blank blank row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g ring operator h close parentheses open parentheses x close parentheses end cell row blank equals cell f open parentheses x squared minus 1 close parentheses end cell row blank equals cell 4 open parentheses x squared minus 1 close parentheses end cell row blank equals cell 4 x squared minus 4 end cell end table end style 

Menentukan begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style 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 x minus 1 close parentheses end cell row blank equals cell 4 open parentheses x minus 1 close parentheses end cell row blank equals cell 4 x minus 4 end cell row blank blank blank row cell open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end cell equals cell h open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell row blank equals cell h open parentheses 4 x minus 4 close parentheses end cell row blank equals cell open parentheses 4 x minus 4 close parentheses squared end cell row blank equals cell 16 x squared minus 32 x plus 16 end cell end table end style 

Menentukan begin mathsize 14px style open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator f close parentheses open parentheses x close parentheses end cell equals cell h open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell h open parentheses 4 x close parentheses end cell row blank equals cell open parentheses 4 x close parentheses squared end cell row blank equals cell 16 x squared end cell row blank blank blank row cell open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses h ring operator f close parentheses open parentheses x close parentheses end cell row blank equals cell g open parentheses 16 x squared close parentheses end cell row blank equals cell 16 x squared minus 1 end cell end table end style 

Maka 

begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses minus open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses plus open parentheses g ring operator h ring operator f close parentheses open parentheses x close parentheses equals open parentheses 4 x squared minus 4 close parentheses minus open parentheses 16 x squared minus 32 x plus 16 close parentheses plus open parentheses 16 x squared minus 1 close parentheses equals 4 x squared plus 32 x minus 21 end style  

Jadi begin mathsize 14px style left parenthesis f ring operator g ring operator h right parenthesis left parenthesis x right parenthesis minus left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis plus left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis equals 4 x squared plus 32 x minus 21 end style. 

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