Any function f (x) defined on R can be expressed as the sum of an odd function g (x) and an even function H (x), if f (x) = LG (x times of 10 + 1), X The analytic expressions of G (x), H (x) belong to R Thank you very much. I hope you can answer quickly

Any function f (x) defined on R can be expressed as the sum of an odd function g (x) and an even function H (x), if f (x) = LG (x times of 10 + 1), X The analytic expressions of G (x), H (x) belong to R Thank you very much. I hope you can answer quickly

f(x)=[f(x)-f(-x)]/2+[f(x)+f(-x)]/2
G (x) = [f (x) - f (- x)] / 2, odd function
H (x) = [f (x) + F (- x)] / 2, even function
If f (x) = LG (10 ^ x + 1), then G (x) = x / 2, H (x) = 1 / 2 × LG (2 + 10 ^ x + 10 ^ (- x))