Jika dik. g(x)=2x²+x-2,tentukan f(x) sehingga: a.(fog)(x)=4x²+2x-5 b.(gof)(x)=8x²-6x-1 Tolong bantu jawab..

jawab

g(x) = 2x² + x - 2

a) (fog)(x) = 4x² + 2x - 5
f(2x² + x -2) = 4x² +2x - 5
f(2x² + x - 2) = 2(2x² +x -2)  -1
f(x)= 2x - 1

b) gof(x) = 8x²-6x -1
misal f(x) = ax + b
g{(ax +b)} = 8x² - 6x - 1
2 (ax+b)² + (ax + b)  - 2 = 8x² -6x - 1
2(a²x² + 2 abx +b²) + ax + b - 2 = 8x² -6x - 1
2a² x² + 4 ab x + 2b² + ax + b - 2 = 8x² -6x - 1
(2a²) x² + (4ab +a) x + (2b²+b - 2) = 8x² -6x - 1
2a² = 8
a= 2

4ab + a = -6
4(2)(b) +(2)= - 6
8b = -6 -2
b = -1
f(x) = ax + b
f(x)= 2x -1