Pertanyaan

Diketahui f ( x ) = x − 2 x dan g ( x ) = x x + 2 . Nilai ( g f ) ( 1 ) ( f + g ) ( 4 ) × ( f − g ) ( 3 ) adalah...

Diketahui $f (x) = \frac{x}{x - 2}$ dan $g (x) = \frac{x + 2}{x}$ . Nilai $\frac{( f + g ) ( 4 ) \times ( f - g ) ( 3 )}{( \frac{f}{g} ) ( 1 )}$ adalah...

F. Ayudhita

Master Teacher

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Pembahasan

Diketahui dan . menggunakan konsep penjumlahan, perkalian, pengurangan, dan pembagian fungsi : = kita cari dulu nilai fungsinya maka, = jadi, jawabannya

Diketahui $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x over denominator x minus 2 end fraction end style$ dan $begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator x plus 2 over denominator x end fraction end style$ .

menggunakan konsep penjumlahan, perkalian, pengurangan, dan pembagian fungsi :

$begin mathsize 14px style fraction numerator open parentheses f plus g close parentheses open parentheses 4 close parentheses cross times open parentheses f minus g close parentheses open parentheses 3 close parentheses over denominator open parentheses begin display style f over g end style close parentheses open parentheses 1 close parentheses end fraction end style$ = $begin mathsize 14px style fraction numerator left parenthesis f left parenthesis 4 right parenthesis plus g left parenthesis 4 right parenthesis right parenthesis cross times left parenthesis f left parenthesis 3 right parenthesis minus g left parenthesis 3 right parenthesis right parenthesis over denominator begin display style fraction numerator f left parenthesis 1 right parenthesis over denominator g left parenthesis 1 right parenthesis end fraction end style end fraction end style$

kita cari dulu nilai fungsinya

$begin mathsize 14px style f left parenthesis 1 right parenthesis equals fraction numerator 1 over denominator 1 minus 2 end fraction equals negative 1 f left parenthesis 3 right parenthesis equals fraction numerator 3 over denominator 3 minus 2 end fraction equals 3 f left parenthesis 4 right parenthesis equals fraction numerator 4 over denominator 4 minus 2 end fraction equals 2 g left parenthesis 1 right parenthesis equals fraction numerator 1 plus 2 over denominator 1 end fraction equals 3 g left parenthesis 3 right parenthesis equals fraction numerator 3 plus 2 over denominator 3 end fraction equals 5 over 3 g left parenthesis 4 right parenthesis equals fraction numerator 4 plus 2 over denominator 4 end fraction equals 6 over 4 end style$

maka,

$begin mathsize 14px style fraction numerator left parenthesis f left parenthesis 4 right parenthesis plus g left parenthesis 4 right parenthesis right parenthesis cross times left parenthesis f left parenthesis 3 right parenthesis minus g left parenthesis 3 right parenthesis right parenthesis over denominator begin display style fraction numerator f left parenthesis 1 right parenthesis over denominator g left parenthesis 1 right parenthesis end fraction end style end fraction end style$ = $begin mathsize 14px style fraction numerator open parentheses 2 plus begin display style 3 over 2 end style close parentheses cross times open parentheses 3 minus begin display style 5 over 3 end style close parentheses over denominator begin display style fraction numerator negative 1 over denominator 3 end fraction end style end fraction equals fraction numerator begin display style 7 over 2 end style cross times begin display style 4 over 3 end style over denominator begin display style fraction numerator negative 1 over denominator 3 end fraction end style end fraction equals 14 over 3 cross times fraction numerator 3 over denominator negative 1 end fraction equals negative 14 end style$

jadi, jawabannya

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