F (1-2x) = (1-x ^ 2) / x ^ 2, if x is not equal to 0, find f (x)

F (1-2x) = (1-x ^ 2) / x ^ 2, if x is not equal to 0, find f (x)

Substitution, let t = 1-2x, x = (1-T) / 2, bring in the original formula, and you can calculate it yourself

If 2F (x) + F (1 / x) = 2x + 1 / 2 (x is not equal to 0), then f (2)=

2f(x)+f(1/x)=2x+1/2
If x = 2, then 2F (2) + F (1 / 2) = 4 + 1 / 2 = 9 / 2 (1)
If x = 1 / 2, then 2F (1 / 2) + F (2) = 1 + 1 / 2 = 3 / 2 (2)
From (1) × 2 - (2), 4f (2) - f (2) = 9-3 / 2
3f(2)=15/2
f(2)=5/2

Given the function g (x) = 1-2x, f [g (x)] = (1-x ^ 2) / x ^ 2 (x is not equal to 0), then f (x) is equal to?
Thank you very much
Find f (0)

Let a = g (x) = 1-2x
x=(1-a)/2
So f (a) = (1-x ^ 2) / x ^ 2 = 1 / x ^ 2-1 = 1 / [(1-A) ^ 2 / 4] - 1 = 4 / (a ^ 2-2a + 1) - 1
So f (x) = 4 / (x ^ 2-2x + 1) - 1 = (- x ^ 2 + 2x + 3) / (x ^ 2-2x + 1)
Let g (x) = 1-2x = 0, x = 1 / 2
So f (0) = (1-x ^ 2) / x ^ 2 = 1 / x ^ 2-1 = 1 / (1 / 4) - 1 = 3