jika g(x)=x+1 dan (fog)(x)=x2+3x+1,maka f(x).....

g(x)=x+1
g^-1(x)=x-1
f(x)og(x)=x²+3x+1
f(x)=(x²+3x+1)og^-1(x)
f(x)=(x-1)²+3(x-1)+1
f(x)=x²-2x+1+3x-3+1
f(x)=x²+x-1

jawab

cara yng lain

krn g(x)  linier
dan fog(x)  kuadrat
maka f(x)  fungsi kuadrat
misal f(x) =ax² + bx + c

g(x) = x + 1
fog(x) = x² + 3x + 1
f(x+1)  = x² + 3x + 1
a(x+1)² + b(x + 1) + c = x² + 3x + 1
ax² + 2ax + a + bx+ b + c = x² + 3x + 1
ax² + (2a + b) x + (a+ b+c) = x² + 3x + 1
a = 1
2a + b = 3 → 2(1) + b = 3
b = 1
a + b + c = 1
1 + 1 + c = 1
c = -1

f(x) = ax² + bx + c
f(x) = x² + x - 1