Question

Diketahui f(x) = 2x-7 dan g(x) = xpangkat2 + 2x - 3.
Ditanya : lim x mendekati 0 = (fog)(x+h)-(fog)(x) / h =

Tolong saya dong...
jangan lupa pakai caranya juga yaa..

Answer 1

F(x) = 2x-7
g(x) = x²+2x+3
maka
(fog)(x) = 2 (x²+2x+3) - 7
           = 2x² + 4x + 6 - 7
           = 2x² + 4x - 1
(fog)(x+h) = 2(x+h)² + 4(x+h) - 1
               = 2 (x² + 2hx + h²) + 4x +4h - 1
               = 2x² + 4hx + 4x + 2h² + 4h -1
               = 2x² + 4hx + 4x + 2h²+4h-1

lim h ->0  (fog)(x+h)-(fog)(x) / h
= lim h ->0  2x² + 4hx + 4x + 2h²+4h-1 -  (2x² + 4x - 1)  / h
= lim h ->0  2x² + 4hx + 4x + 2h²+4h-1 -  2x² - 4x + 1  / h
= lim h->0  4hx + 2h² +  4h / h
= lim h->0  4x + 2h + 4
= 4x + 2.0 + 4
= 4x + 4