Pertanyaan

Diketahui g ( x ) = 3 x + 2 dan ( f ∘ g ) ( x ) = 3 x + 1 3 x + 2 ; x  = 3 1 . Rumus fungsi f ( x ) = ....

Diketahui $g (x) = 3 x + 2$ dan $(f \circ g) (x) = \frac{3 x + 2}{3 x + 1}$ ; $x \neq = \frac{1}{3}$ . Rumus fungsi $f (x) =$ ....

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Jawaban terverifikasi

Jawaban

rumus fungsi yang diperoleh adalah .

rumus fungsi yang diperoleh adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator x minus 1 end fraction end cell end table end style$ .

Pembahasan

Perhatikan misal , maka Jadi, rumus fungsi yang diperoleh adalah .

Perhatikan

misal $begin mathsize 14px style a equals 3 x plus 2 comma space fraction numerator a minus 2 over denominator 3 end fraction equals x end style$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 2 over denominator 3 x plus 1 end fraction end cell row cell f open parentheses 3 x plus 2 close parentheses end cell equals cell fraction numerator 3 x plus 2 over denominator 3 x plus 1 end fraction end cell row cell f open parentheses a close parentheses end cell equals cell fraction numerator 3 open parentheses begin display style fraction numerator a minus 2 over denominator 3 end fraction end style close parentheses plus 2 over denominator 3 open parentheses begin display style fraction numerator a minus 2 over denominator 3 end fraction end style close parentheses plus 1 end fraction end cell row cell f open parentheses a close parentheses end cell equals cell fraction numerator a minus 2 plus 2 over denominator a minus 2 plus 1 end fraction end cell row cell f open parentheses a close parentheses end cell equals cell fraction numerator a over denominator a minus 1 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator x over denominator x minus 1 end fraction end cell end table end style$

Jadi, rumus fungsi yang diperoleh adalah $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator x minus 1 end fraction end cell end table end style$ .