Concepts and symbols:

The concept of function.

Generally speaking, we have: Let A and B be numbers of nonempty sets. If any number X in set A has a unique number f(x) corresponding to it according to a certain correspondence F, then f:A→B is called a function from set A to set B, and it is denoted as: y=f(x), x \

The concept of mapping.

Generally speaking, we have: Let A and B be two nonempty sets. If any element X in set A has a unique element Y corresponding to it according to a certain correspondence F, then the correspondence f:A→B is called the mapping from set A to set B.

The maximum value of the function.

Generally, let the domain of the function y=f(x) be I, and if there is a real number m satisfying:

(1) For any x EI, there is f(x)≤M(f(x)≥M).

(2) xo∈ 1 exists, so f (XO) = m.

Then say that m is the maximum (minimum) value of the function y=f(x), which is usually recorded as:

Ymax = M or f(x)max = M(ymin = M or f(x)min=M).

Equivalent form of even-odd function equation;

Odd function f(-x)=-f(ox)f(-x)+f(x)=0.

f(-x)/fx=- 1(f(x)≠0(x).

Even function f(-x)=f(x)=f(-x)-f(x)=0.

f(-x)/fx= 1(f(x)≠0(x).

Commonly used formulas.

Logarithmic identity:

Functional application:

Commonly used formula:

Common theorems:

Existence theorem of zero point;

Generally speaking, we have: If the image of the function y=f(x) in the interval [a, b] is a continuous curve with f (a). f (b)

Operation steps of dichotomy:

Given the accuracy e, the steps of finding the approximate value of the zero point of the function f(x) in the interval [a, b] by dichotomy are as follows:

(1) Determine the interval [a, b] and verify f (a). f (b)

(2) Find the midpoint c of the interval (a, b).

(3) calculate f(c).

(1) If f(c)=0, then c is the zero point of the function.

② If f (a). f (c)

③ If f (c)。 f (b)