1. 反函数

定义1：

A function ƒ is called a one-to-one function if it never takes on the same value twice;

that is ƒ(x₁)≠ƒ(x₂) whenever x₁≠x₂.

Horizontal Line Test:

A function is one-to-one if and only if no horizontal line intersects its graph more than once.

水平线测试：one-to-one的函数在一条水平线上只能产生一个交点。

定义2：反函数

Let ƒ be a one-to-one function with domain A and range B. Then its inverse function ƒ^-1 has domain B and range A and is defined by

ƒ^-1(y)=x ↔ ƒ(x)=y;

then

ƒ^-1(ƒ(x))=x

ƒ(ƒ^-1(x))=x

2. 三角函数的反函数

三角函数本身并不是one-to-one的，但是可以通过限定区间把它变成one-to-one

3. 不定式与洛必达法则