Pertanyaan

Diketahui f ( x + 5 ) = 3 x 2 + 10 x − 3 dan g ( 4 x − 1 ) = 2 x + 2 1 − 8 x . Tentukan hasil berikut 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 hasil berikut

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

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Jawaban terverifikasi

Jawaban

adalah

$begin mathsize 14px style fraction numerator 3 g over denominator f end fraction open parentheses x close parentheses end style$ adalah $begin mathsize 14px style fraction numerator negative 9 x plus 3 over denominator left parenthesis x plus 5 right parenthesis left parenthesis 3 x squared plus 55 x plus 47 right parenthesis end fraction. end style$

Pembahasan

Jadi, adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 g over denominator f end fraction open parentheses x close parentheses end cell equals cell fraction numerator 3 open parentheses begin display style fraction numerator negative 3 x plus 1 over denominator x plus 5 end fraction end style close parentheses over denominator 3 x squared plus 55 x plus 47 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 9 x plus 3 over denominator x plus 5 end fraction end style over denominator 3 x squared plus 55 x plus 47 end fraction end cell row blank equals cell fraction numerator negative 9 x plus 3 over denominator x plus 5 end fraction times fraction numerator 1 over denominator 3 x squared plus 55 x plus 47 end fraction end cell row cell fraction numerator 3 g over denominator f end fraction open parentheses x close parentheses end cell equals cell fraction numerator negative 9 x plus 3 over denominator open parentheses x plus 5 close parentheses open parentheses 3 x squared plus 55 x plus 47 close parentheses end fraction end cell end table end style$

Jadi, $begin mathsize 14px style fraction numerator 3 g over denominator f end fraction open parentheses x close parentheses end style$ adalah $begin mathsize 14px style fraction numerator negative 9 x plus 3 over denominator left parenthesis x plus 5 right parenthesis left parenthesis 3 x squared plus 55 x plus 47 right parenthesis end fraction. end style$