Neka je f (x) = 3x ^ 2-x + 2 i g (x) = 5x ^ 2-1. Što je f (g (x))?

Neka je f (x) = 3x ^ 2-x + 2 i g (x) = 5x ^ 2-1. Što je f (g (x))?
Anonim

Odgovor:

#F (g (x)) = 75x ^ 4-35x ^ 2 + 6 #

Obrazloženje:

# "da dobijemo" f (g (x)) "zamijeni" g (x) "u" f (x) #

#rArrf (g (x)) *

# = F (boja (crvena) (5x ^ 2-1)) = 3 (boja (crvena) (5x ^ 2-1)) ^ 2- (boja (crvena) (5x ^ 2-1)) + 2 #

# = 3 (25x ^ 4-10x ^ 2 + 1) -5x ^ 2 + 1 + # 2

# = 75x ^ 4-30x ^ 2 + 3-5x ^ 2 + 1 + # 2

# = 75x ^ 4-35x ^ 2 + 6 #