Tentukan (fog)(x) dan (gof)(1) jika 1. f(x)=x²-x-6, g(x)=x²+2 2. f(x)=x-1/3x+5, g(x)=2x-6 3. f(x)=x-6/2x+2, g(x)=5/1-2x
Matematika
Avitry
Pertanyaan
Tentukan (fog)(x) dan (gof)(1) jika
1. f(x)=x²-x-6, g(x)=x²+2
2. f(x)=x-1/3x+5, g(x)=2x-6
3. f(x)=x-6/2x+2, g(x)=5/1-2x
1. f(x)=x²-x-6, g(x)=x²+2
2. f(x)=x-1/3x+5, g(x)=2x-6
3. f(x)=x-6/2x+2, g(x)=5/1-2x
1 Jawaban
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1. Jawaban rifkyulliyah
1.) (f°g)(x) = (x²+2)²-(x²+2)-6 = x⁴+4x²+4-x²-2-6 = x⁴+3x²-4
(g°f)(1) = (x²-x-6)²+2 = x⁴-x³-6x²-x³+x²+6x-6x²+6x+36+2 = x⁴-2x³-11x²-12x+38 = 1⁴-2.1³-11.1²-12.1+38 = 14
2.) (f°g)(x) = 2x-6-1/ 3(2x-6)+5 = 2x-7/6x-18+5 = 2x-7/6x-13
(g°f)(1) = 2(x-1/3x+5)-6 = 2x-2/3x+5 - 6 = 2.1-2/3.1+5 - 6 = 0/8 - 6 = 0-6 = -6
Yang tiganya coba cari sendiri:)
Semoga bermanfaat yaa .. Saya sudah ngantuk .. Hehe