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f ( x ) = x − 4 , g ( x ) = x − 5 11 x + 4 ​ , x  = 5 Tentukan ( g ∘ f ) ( x ) dan ( g ∘ f ) ( − 1 )

 

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S. Nur

Master Teacher

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dan .

 open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 11 x minus 40 over denominator x minus 5 end fraction space dan open parentheses g ring operator f close parentheses open parentheses negative 1 close parentheses equals 51 over 6.

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Jadi, dan .

f open parentheses x close parentheses equals x minus 4 comma space g open parentheses x close parentheses equals fraction numerator 11 x plus 4 over denominator x minus 5 end fraction comma space x not equal to 5 open parentheses g ring operator f close parentheses open parentheses x close parentheses equals g open parentheses f open parentheses x close parentheses close parentheses space space space space space space space space space space space space space equals g open parentheses x minus 4 close parentheses space space space space space space space space space space space space space equals fraction numerator 11 open parentheses x minus 4 close parentheses plus 4 over denominator x minus 5 end fraction space space space space space space space space space space space space space equals fraction numerator 11 x minus 44 plus 4 over denominator x minus 5 end fraction space space space space space space space space space space space space space equals fraction numerator 11 x minus 40 over denominator x minus 5 end fraction space space space space space space space space space space space space space rightwards arrow space space space space space open parentheses g ring operator f close parentheses open parentheses negative 1 close parentheses equals fraction numerator 11 open parentheses negative 1 close parentheses minus 40 over denominator negative 1 minus 5 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 51 over denominator negative 6 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 51 over 6 

Jadi, open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 11 x minus 40 over denominator x minus 5 end fraction space dan open parentheses g ring operator f close parentheses open parentheses negative 1 close parentheses equals 51 over 6.

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Diketahui f : R → R dan g : R → R dengan f ( x ) = x 2 + 5 dan g ( x ) = x − 3 . Tentukanlah nilai yang memenuhi: ( f ∘ g ) ( a ) = ( g ∘ f ) ( a ) .

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