(g○f)(x)=2x^2-2x+2 f(x)=x+2 g(x)=?

(g○f)(x)=2x^2-2x+2

f(x)=x+2

g(x)=....

jawab :

(g○f) = g(f(x))

g(x+2) = 2x^2 - 2x + 2

misal g(x) = ax^2 + bx + c ... karena g(x) pada soal berderajat 2

maka

a = 2 ✔

2 (x+2)^2 + b (x+2) + c = 2 ( x^2 + 4x + 4 ) + bx + 2b + c

2x^2 + 8x + 8 + bx + 2b + c

kita cari nilai b

8x + bx = -2

b = -10 ✔

dan mencari c

2b + c = 2
2.(-10) + c = 2
-20 + c = 2

c = 22 ✔

sehingga g(x) = 2x^2 - 10x + 22 ✔

semoga membantu