It is known that y = f (x) is an even function defined on R When x is greater than or equal to 0, f (x) = x ^ 2-2x. Find the analytic expression of F (x) when x is less than or equal to 0

It is known that y = f (x) is an even function defined on R When x is greater than or equal to 0, f (x) = x ^ 2-2x. Find the analytic expression of F (x) when x is less than or equal to 0

Let x0 be defined by the function greater than
f(-x)=(-x)^2+2x=x^2+2x
Because it's an even function, so
When x

If y = f (x) is an even function on R and f (x + 1) = 1 / F (x), then the period of y = f (x) is

f(x+1)=1/f(x),
Let x = x + 1
Then f (x + 2) = 1 / F (x + 1) = 1 / (1 / F (x)) = f (x)
So the period is two

My child is studying hard in grade one of senior high school. There is a math problem that doesn't understand its meaning. Please give me your advice!
Given that f (x) is an even function, G (x) is an odd function and f (x) + G (x) = (2 / 3 power of X + 1) (x-1 power + 3), then f (x) = g (x)=

If f (x) is an odd function, G (x) is an even function, and f (x) + G (x) = f (x). (1) then f (- x) + G (- x) = f (- x), i.e. - f (x) + G (x) = f (- x). (2) simultaneous (1) (2) two expressions (i.e. addition) give g (x) = [f (x) + F (- x)] / 2