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High school mathematics solution function
Because when x belongs to 2,3, f(x) is equal to x and f(x) is an even function,

So when x belongs to -3, -2, f(x) equals X.

For any x belonging to r, f(x) is equal to f(x+2),

So when x belongs to-1, 0, f(x) equals x, (conclusion 1).

Because f(x) is an even function,

So when x belongs to 0, 1, f(x) equals x,

That is, when x belongs to-1 and 1, f(x) equals x,

For any X belonging to R, f(x) is equal to f(x+2).

When x belongs to -3,-1, f(x) is equal to x (conclusion 2).

Comprehensive conclusion one conclusion two, when x belongs to-2,0, the analytical formula for finding f(x) is f (x) = X