Let f (x) = 3x + 1 dengan f: R -> R. Tentukan fungsi linear h: R -> R sedemikian rupa sehingga: h (f (x)) = 6x - 1?

Jawapan:

#h (x) = 2x-3 #

Penjelasan:

# "kerana" h (x) "adalah fungsi linear" #

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

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

#color (putih) (rArrh (f (x))) = 3ax + a + b #

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

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

#color (biru) "bandingkan pekali istilah seperti" #

# rArr3a = 6rArra = 2 #

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

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