Pertanyaan

Diketahui f ( x ) = x − 1 x + 2 dan g ( x ) = x + 3 2 x + 1 . Fungsi komposisi ( f ∘ g ) ( x ) = ... .

Diketahui $f (x) = \frac{x + 2}{x - 1}$ dan $g (x) = \frac{2 x + 1}{x + 3}$ . Fungsi komposisi $(f \circ g) (x) = ...$ .

$fraction numerator 4 x plus 7 over denominator x minus 2 end fraction$
$fraction numerator 4 x plus 7 over denominator x plus 3 end fraction$
$fraction numerator x plus 3 over denominator x minus 2 end fraction$
$fraction numerator 2 x minus 1 over denominator x plus 7 end fraction$
$fraction numerator x minus 2 over denominator 4 x plus 7 end fraction$

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Habis dalam

Klaim

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Komposisi dua fungsi. Diketahui dan , akan ditentukan fungsi komposisi . Jadi, jawaban yang tepat adalah A.

Komposisi dua fungsi.

Diketahui $f open parentheses x close parentheses equals fraction numerator x plus 2 over denominator x minus 1 end fraction$ dan $g open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x plus 3 end fraction$ , akan ditentukan fungsi komposisi open parentheses f ring operator g close parentheses open parentheses x close parentheses .

$table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses fraction numerator 2 x plus 1 over denominator x plus 3 end fraction close parentheses end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction end style plus 2 over denominator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction end style minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction plus fraction numerator 2 open parentheses x plus 3 close parentheses over denominator x plus 3 end fraction end style over denominator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction minus fraction numerator begin display style open parentheses x plus 3 close parentheses end style over denominator x plus 3 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction plus fraction numerator 2 x plus 6 over denominator x plus 3 end fraction end style over denominator begin display style fraction numerator 2 x plus 1 over denominator x plus 3 end fraction minus fraction numerator begin display style open parentheses x plus 3 close parentheses end style over denominator x plus 3 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 4 x plus 7 over denominator x plus 3 end fraction end style over denominator begin display style fraction numerator x minus 2 over denominator x plus 3 end fraction end style end fraction end cell row blank equals cell fraction numerator 4 x plus 7 over denominator up diagonal strike x plus 3 end strike end fraction cross times fraction numerator up diagonal strike x plus 3 end strike over denominator x minus 2 end fraction end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 4 x plus 7 over denominator x minus 2 end fraction end cell end table$

Jadi, jawaban yang tepat adalah A.