Chapter (7)--Inverse Functions inverse function

1. Inverse function

Definition 1:

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

That isƒ (x1) ≠ƒ (x2) whenever x1≠x2.

Horizontal line Test:

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

Horizontal line test: The one-to-one function can produce only one intersection point on a horizontal level.

Definition 2: Inverse function

Letƒbe a one-to-one function with domain A and range B. Then its inverse functionƒ-1 have domain B and range A and are defined by

Ƒ-1 (y) =x↔ƒ (x) =y;

Then

Ƒ-1 (ƒ (x)) =x

ƒ (ƒ-1 (x)) =x

2. Inverse function of trigonometric functions

The trigonometric functions themselves are not one-to-one, but can be transformed into one-to-one by limiting the interval.

3. Infinitive and indeterminate form law

Chapter (7)--Inverse Functions inverse function