injective, surjective既分別??

injective
一個y值對應的只有一個x值
如y=x -> 在線圖上,只有係x=3,才能出現y=3 ,其它的x值(唔等於3)不會出現y=3這情況,呢個函數就係injective
如y=x^2 ->這個不是injective...因為對於一個y值...如y=1,對應的x值有2個,分別係1同-1
surjective
對於每一個y值,都會有對應的x值
如y=x...對每一個y值,都會有對應的x值
但是對於y=sinx...由於y的範圍係-1至1之間...所以如果當y=3,係冇一個x值能令y=3的...所以呢個函數係not surjective
bijective
若一個函數既有injective,又有surjective...咁就叫bijective

2009-03-29 14:44:15 補充：
Yes!

Definition:
injective - For all a, b in the domain, f(a) = f(b) implies a = b.
surjective - For all y in the codomain, there exists an x in the domain s.t. f(x) = y.

談及 mapping，必須說明 domain及 codomain。
y = f(x) = x^2 的 domain（x 的取值）若為 非負實數，codomain（y / f(x) 的取值）亦為 非負實數，且 f 為 bijective。

injective 同 surjective 係不一樣。
Examples:
injective and surjective, .i.e. bijective - f: R→R s.t. f(x) = x
injective but not surjective - f: R→R s.t. f(x) = 2^x
surjective but not injective - f: R→R s.t. f(x) = tan(x)
not injective and not surjective - f: R→R s.t. f(x) = sin(x)

咁injective同surjective係一樣???都係可以運用起y=x呢條formula度???
for injective, 當x=1, y=1
for surjective, 當x=1, y=1
so formula y=x 係bijective?