Pertanyaan

Diketahui: f ( x ) g ( x ) = = 2 x − 5 x + 2 dan 3 x + 7 2 x Tentukan fungsi komposisi berikut: b. ( g ∘ f ) ( x )

Diketahui:

$f (x) g (x) = = \frac{x + 2}{2 x - 5} dan \frac{2 x}{3 x + 7}$

Tentukan fungsi komposisi berikut:

b. $(g \circ f) (x)$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x plus 4 over denominator 17 x minus 29 end fraction end cell end table end style$ .

Pembahasan

Dengan menerapkan konsep komposisi dua fungsi, diperoleh perhitungan sebagai berikut. Jadi, .

Dengan menerapkan konsep komposisi dua fungsi, diperoleh perhitungan sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator 2 f open parentheses x close parentheses over denominator 3 f open parentheses x close parentheses plus 7 end fraction end cell row blank equals cell fraction numerator 2 open parentheses begin display style fraction numerator x plus 2 over denominator 2 x minus 5 end fraction end style close parentheses over denominator 3 open parentheses begin display style fraction numerator x plus 2 over denominator 2 x minus 5 end fraction end style close parentheses plus 7 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 4 over denominator 2 x minus 5 end fraction end style over denominator begin display style fraction numerator 3 x plus 6 over denominator 2 x minus 5 end fraction end style plus begin display style fraction numerator 14 x minus 35 over denominator 2 x minus 5 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 4 over denominator 2 x minus 5 end fraction end style over denominator begin display style fraction numerator 17 x minus 29 over denominator 2 x minus 5 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 x plus 4 over denominator up diagonal strike 2 x minus 5 end strike end fraction cross times fraction numerator up diagonal strike 2 x minus 5 end strike over denominator 17 x minus 29 end fraction end cell row blank equals cell fraction numerator 2 x plus 4 over denominator 17 x minus 29 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses g ring operator f close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x plus 4 over denominator 17 x minus 29 end fraction end cell end table end style$ .