Analyze the topic first.

This topic gives two known conditions.

①f(4-x)=f(ⅹ-2)

②f( 1)=2

Our way of thinking to solve the problem should proceed from these two conditions, deduce and finally get the answer.

The first condition is to derive the symmetry axis of y=f(ⅹ), thus simplifying the function from 1 to 202 1 according to the symmetry relation.

The following is the formula of its symmetry axis (selected from "Required Questions for Senior High School" and "Crazy K Focus" on page 4 1).

According to the conditions given in the title, the third formula should be used here.

Then the symmetry axis x = (a+b)/2 = (4-2) ÷ 2 = 1.

Then you can get:

So we know that every four numbers have a cycle.

That is, f (1)+f (2)+f (3)+f (4) ...+f (2021) = f (2021) = 2.

Therefore, this question should choose B.

Knowledge expansion:

Basic nature:

Generally speaking, if any x in the definition domain of the function f(x) has f (-x) = f(x), then the function f(x) is called an even function.

Generally speaking, if any x in the definition domain of the function f(x) has f (-x) =-f(x), then the function f(x) is called odd function.

Image features:

Theorem: odd function's image is centrosymmetric about the origin, and even function's image is axisymmetrical about Y ..

Inference: If there is f(a+x)+f(b-x)=c for any x, then the function image is symmetric about (a/2+b/2, c/2);

If there is f(a+x)=f(a-x) for any x, the function image is symmetric about x = a.

Odd function's image is symmetrical about the origin.

Point (x, y)(-x, -y)

The image of even function is symmetric about y.

Point (x, y)(-x, y)

Odd function monotonically increases in a certain interval and monotonically increases in its symmetric interval.

Even function monotonically increases in a certain interval, but monotonically decreases in its symmetric interval.

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