Naj bo f (x) = 3x + 1 z f: R -> R. Poišči linearno funkcijo h: R -> R tako, da: h (f (x)) = 6x - 1?

Odgovor:

#h (x) = 2x-3 #

Pojasnilo:

# "od" h (x) "je linearna funkcija" #

# "let" h (x) = ax + b #

#rArrh (f (x)) = a (3x + 1) + b #

#barva (bela) (rArrh (f (x))) = 3ax + a + b #

.# "zdaj" h (f (x)) = 6x-1 #

# rArr3ax + a + b = 6x-1 #

#color (modra) "primerjaj koeficiente podobnih izrazov" #

# rArr3a = 6rArra = 2 #

# a + b = -1rArr2 + b = -1rArrb = -3

#rArrh (x) = ax + b = 2x-3 #