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Diketahui f ( x ) = 5 − 8 x , tentukan : b). g ( x ) jika ( g ∘ f ) ( x ) = 5 x − 5

Diketahui , tentukan :

b).  jika   

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Diketahui : Ditanya : ? Jawab : Cari invers terlebih dulu Kemudian cari

Diketahui :

begin mathsize 14px style f left parenthesis x right parenthesis equals 5 minus 8 x end style

size 14px left parenthesis size 14px g size 14px ring operator size 14px f size 14px right parenthesis begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px 5 size 14px x size 14px minus size 14px 5  

Ditanya :

begin mathsize 14px style g left parenthesis x right parenthesis end style?

Jawab :

undefined   

Cari invers begin mathsize 14px style bold f bold left parenthesis bold x bold right parenthesis end style terlebih dulu

begin mathsize 14px style space space space space space f open parentheses x close parentheses equals 5 minus 8 x space space space space space space space space space y equals 5 minus 8 x space space space space space space space 8 x equals 5 minus y space space space space space space space space space x equals fraction numerator 5 minus y over denominator 8 end fraction f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 5 minus x over denominator 8 end fraction end style 

Kemudian cari begin mathsize 14px style bold g bold left parenthesis bold x bold right parenthesis end style 

 begin mathsize 14px style g left parenthesis x right parenthesis equals left parenthesis g ring operator f right parenthesis left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis g left parenthesis x right parenthesis equals left parenthesis 5 left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis minus 5 g left parenthesis x right parenthesis equals 5 open parentheses fraction numerator 5 minus x over denominator 8 end fraction close parentheses minus 5 g left parenthesis x right parenthesis equals open parentheses fraction numerator 25 minus 5 x over denominator 8 end fraction close parentheses minus 5 g left parenthesis x right parenthesis equals fraction numerator x minus 15 over denominator 8 end fraction end style 

 

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Diketahui fungsi f ( x + 1 ) = f ( x ) + 1 , g ( x + 1 ) = g ( x ) − 1 , f ( 1 ) = 1 , dan g ( 1 ) = 1 . Tentukan nilai f ( 2.000 ) + g ( 2.000 )

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