Pertanyaan

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 $f (x + 5) = 3 x^{2} + 10 x -3$ dan $g (4 x -1) = \frac{1 - 8 x}{2 x + 2}$ . Tentukan:

d. $(\frac{3 g}{f}) (x)$

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

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

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