Keď f (x) = 25-x ^ 2 a g (x) = x + 5, (f / g) (x) = ___?

odpoveď:

# 5-x #

vysvetlenie:

# (f / g) x = f (x) / g (x) #

#f (x) = 25 - x ^ 2 #

rozdiel identity dvoch štvorcov: # a ^ 2 - b ^ 2 = (a + b) (a-b) #

# 25 - x ^ 2 = 5 ^ 2 - x ^ 2 #

# = (5 + x) (5-x) #

#g (x) = x + 5 alebo 5 + x #

#f (x) / g (x) = ((5 + x) (5-x)) / (x + 5) #

# = (5-x) / 1 = 5-x #