diketahui f(x) = x²+x+1 dan f(g(x)) = 4x²+6x+3. tentukan rumus fungsi g(x)

jawab


f(x)= x² + x  + 1
f{g(x)} = 4x²+ 6x + 3
misalkan
g(x)= ax + b

f (ax+ b) = 4x² + 6x + 3
(ax+b)² +(ax + b) + 1 = 4x²+ 6x + 3
a²x² + 2abx + b² + ax + b = 4x² + 6x  + 3

a²= 4
a= 2

2ab+ a = 6
2(2)b+ 2= 6
4b = 4
b = 1

g(x) = ax + b
g(x)= 2x + 1

f(g(x)) = 4x² + 6x + 3
g(x)² + g(x) + 1 = 4x² + 6x +3
g(x)² + g(x) = 4x² + 6x + 2
g(x)² + g(x) + ¼ = 4x² + 6x + (9/4)
kali 4 smua
4g(x)² + 4g(x) + 1 = 16x² + 24x + 9
(2g(x) + 1)² = (4x + 3)²
2g(x) + 1 = 4x + 3
2g(x) = 4x + 2
g(x) = 2x + 1