函數定義域

1.
f(x): x is [-3, 4)
f(2x-1): 2x-1 is [-3, 4)
=> -3 ≦ 2x-1 < 4
=> -2 ≦ 2x < 5
=> -1 ≦ x < 5/2
So, f(2x-1): x is [-1, 5/2)

2.
f(x) = 1/(x^2-x-2)
f(x) = 1/(x+1)(x-2)
As f(x) is undefined at x = -1 and 2,
f(x): x is R\{-1, 2}, i.e. (-oo, -1)U(-1, 2)U(2, +oo)
定義域不可以包括 -oo 和+oo, 因為定義域兩端必須是一個數.

3.
正比例定義為 y=kx.
y=kx+b or y=kx-b 是線性函數.

4.
log x: x is [0, +oo)
log 3x: 3x is [0, +oo)
0 ≦ 3x
0 ≦ x
So, log 3x: x is [0, +oo)