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Diketahui f ( x + 5 ) = 3 x 2 + 10 x –3 dan g ( 4 x –1 ) = 2 x + 2 1 − 8 x ​ . Tentukan: d. ( f 3 g ​ ) ( x )

Diketahui  dan . Tentukan:

d.  

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N. Puspita

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table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x plus 5 right parenthesis end cell equals cell 3 x squared plus 10 x – 3 end cell row cell misal space t end cell equals cell x plus 5 space rightwards double arrow space x equals t minus 5 end cell row cell f left parenthesis t minus 5 plus 5 right parenthesis end cell equals cell 3 left parenthesis t minus 5 right parenthesis squared plus 10 left parenthesis t minus 5 right parenthesis minus 3 end cell row cell f left parenthesis t right parenthesis end cell equals cell 3 left parenthesis t squared minus 10 t plus 25 right parenthesis plus 10 t minus 50 minus 3 end cell row cell f left parenthesis t right parenthesis end cell equals cell 3 t squared minus 30 t plus 75 plus 10 t minus 50 minus 3 end cell row cell f left parenthesis t right parenthesis end cell equals cell 3 t squared minus 20 t plus 22 end cell row cell f left parenthesis x right parenthesis end cell equals cell 3 x squared minus 20 x plus 22 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 4 x minus 1 right parenthesis end cell equals cell fraction numerator 1 minus 8 x over denominator 2 x plus 2 end fraction end cell row cell misal space 4 x minus 1 end cell equals cell t space rightwards double arrow space x equals fraction numerator t plus 1 over denominator 4 end fraction end cell row cell g left parenthesis 4 cross times fraction numerator t plus 1 over denominator 4 end fraction minus 1 right parenthesis end cell equals cell fraction numerator 1 minus 8 left parenthesis fraction numerator t plus 1 over denominator 4 end fraction right parenthesis over denominator 2 left parenthesis fraction numerator t plus 1 over denominator 4 end fraction right parenthesis plus 2 end fraction end cell row cell g left parenthesis t right parenthesis end cell equals cell fraction numerator 1 minus 2 t minus 2 over denominator begin display style left parenthesis fraction numerator t plus 1 plus 4 over denominator 2 end fraction right parenthesis end style end fraction end cell row cell g left parenthesis y right parenthesis end cell equals cell fraction numerator negative 4 t minus 2 over denominator t plus 5 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator negative 4 x minus 2 over denominator x plus 5 end fraction end cell end table 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 3 g over denominator f end fraction close parentheses left parenthesis x right parenthesis end cell equals cell fraction numerator 3 cross times g left parenthesis x right parenthesis over denominator f left parenthesis x right parenthesis end fraction end cell row blank equals cell fraction numerator 3 open parentheses begin display style fraction numerator negative 4 x minus 2 over denominator x plus 5 end fraction end style close parentheses over denominator 3 x squared minus 20 x plus 22 end fraction end cell row blank equals cell fraction numerator 3 left parenthesis negative 4 x minus 2 right parenthesis over denominator open parentheses x plus 5 close parentheses left parenthesis 3 x squared minus 20 x plus 22 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 12 x minus 6 over denominator left parenthesis x plus 5 right parenthesis left parenthesis 3 x squared minus 20 x plus 22 right parenthesis end fraction end cell end table end style  

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Diketahui f ( x ) = x 2 − 9 dan g ( x ) = x + 3 . Tentukanlah ( g f ​ ) ( x ) .

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