Sei f (x) = 3x ^ 2-x + 2 und g (x) = 5x ^ 2-1. Was ist f (g (x))?

Sei f (x) = 3x ^ 2-x + 2 und g (x) = 5x ^ 2-1. Was ist f (g (x))?
Anonim

Antworten:

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

Erläuterung:

# "um" f (g (x)) "zu erhalten, ersetzen Sie" g (x) "in" f (x) # "

#rArrf (g (x)) #

# = f (Farbe (rot) (5x ^ 2-1)) = 3 (Farbe (rot) (5x ^ 2-1)) ^ 2- (Farbe (rot) (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 #