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Diberikan f ( x ) = x 2 + 2 dan g ( x ) = x 2 − 2 . Hasil dari ( g ∘ f ) ( x ) − ( f ∘ g ) ( x ) = ....

Diberikan  dan . Hasil dari  

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S. Nur

Master Teacher

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Diberikan dan . Dit : Kita cari masing2 komposisi fungsinya. maka : jadi, jawabannya

Diberikan  dan .

Dit :  

Kita cari masing2 komposisi fungsinya.

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals g open parentheses f left parenthesis x right parenthesis close parentheses end style

               begin mathsize 14px style equals g open parentheses x squared plus 2 close parentheses equals open parentheses x squared plus 2 close parentheses squared minus 2 equals x to the power of 4 plus 4 x squared plus 4 minus 2 equals x to the power of 4 plus 4 x squared plus 2 end style

begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis end style

              begin mathsize 14px style equals f left parenthesis g left parenthesis x right parenthesis right parenthesis equals f left parenthesis x squared minus 2 right parenthesis equals left parenthesis x squared minus 2 right parenthesis squared plus 2 equals x to the power of 4 minus 4 x squared plus 4 plus 2 equals x to the power of 4 minus 4 x squared plus 6 end style

maka :

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis minus left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis x to the power of 4 plus 4 x squared plus 2 right parenthesis minus open parentheses x to the power of 4 minus 4 x squared plus 6 close parentheses equals 8 x squared minus 4 end style

jadi, jawabannya  

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Muhammad Adam Rayhan Nst

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Diketahui g ( f ( x ) ) = f ( g ( x ) ) . Jika f ( x ) = 3 x + a dan g ( x ) = 2 x + 70 , maka nilai a = ...

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