תן f (x) = 3x ^ 2-x + 2 ו- g (x) = 5x ^ 2-1. מהו f (g (x))?

תן f (x) = 3x ^ 2-x + 2 ו- g (x) = 5x ^ 2-1. מהו f (g (x))?
Anonim

תשובה:

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

הסבר:

# "כדי לקבל" f (g (x)) "תחליף" g (x) "לתוך" f (x) # #

#rArrf (g (x)) #

# 2) צבע (אדום) (= 5x ^ 2-1) = 3 (צבע אדום) (5x ^ 2-1)) ^ 2 (צבע (אדום) (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 #