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Diketahui f : R → R , g : R → R , dan h : R → R dengan f ( x ) = 3 x − 1 , g ( x ) = x − 2 1 ​ , dan h ( x ) = x 2 − 1 . Tentukan: a. ( ( g ∘ h ) ∘ f ) ( x )

Diketahui , dan  dengan , dan . Tentukan:

a.  

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 open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator negative 4 x squared plus 16 x minus 19 over denominator x squared minus 4 x plus 4 end fraction.

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Pembahasan

Diketahui: , dan Maka: Sehingga: Jadi, .

Diketahui:

f open parentheses x close parentheses equals 3 x minus 1 comma space g open parentheses x close parentheses equals fraction numerator 1 over denominator x minus 2 end fraction, dan h open parentheses x close parentheses equals x squared minus 1 

Maka:

open parentheses g ring operator h close parentheses open parentheses x close parentheses equals g open parentheses h open parentheses x close parentheses close parentheses open parentheses g ring operator h close parentheses open parentheses x close parentheses equals g open parentheses x squared minus 1 close parentheses open parentheses g ring operator h close parentheses open parentheses x close parentheses equals 3 open parentheses x squared minus 1 close parentheses minus 1 open parentheses g ring operator h close parentheses open parentheses x close parentheses equals 3 x squared minus 3 minus 1 open parentheses g ring operator h close parentheses open parentheses x close parentheses equals 3 x squared minus 4 

Sehingga:

open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals open parentheses g ring operator h close parentheses open parentheses f open parentheses x close parentheses close parentheses open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals open parentheses g ring operator h close parentheses open parentheses fraction numerator 1 over denominator x minus 2 end fraction close parentheses open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals 3 open parentheses fraction numerator 1 over denominator x minus 2 end fraction close parentheses squared minus 4 open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals 3 open parentheses fraction numerator 1 over denominator x squared minus 4 x plus 4 end fraction close parentheses minus 4 open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 3 over denominator x squared minus 4 x plus 4 end fraction minus 4 open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 3 minus 4 open parentheses x squared minus 4 x plus 4 close parentheses over denominator x squared minus 4 x plus 4 end fraction open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 3 minus 4 x squared plus 16 x minus 16 over denominator x squared minus 4 x plus 4 end fraction open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator negative 4 x squared plus 16 x minus 19 over denominator x squared minus 4 x plus 4 end fraction 

Jadi, open parentheses open parentheses g ring operator h close parentheses ring operator f close parentheses open parentheses x close parentheses equals fraction numerator negative 4 x squared plus 16 x minus 19 over denominator x squared minus 4 x plus 4 end fraction.

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