(1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2 (1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2, find f (x)

(1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2 (1 / 2) it is known that f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = f (2-x). When x belongs to [0,2], f (x) = 3x + 2, find f (x)

If f (2 + x) = f (2-x), then f (x) = f (4-x)
If f (x) is an even function, then f (- x) = f (x) = f (4-x)
That is, f (x) = f (x + 4)
So f (x) is a function of period 4
x∈[0,2],f(x)=3x+2
x∈[-2,0],f(x)=f(-x)=3(-x)+2=-3x+2
and so on