Let the domain of function be {x | x is not equal to 0} and f (x) - 2F (one part of x) = X. find the analytic expression of function f (x) | Math enthusiast | Mathematical art

Let the domain of function be {x | x is not equal to 0} and f (x) - 2F (one part of x) = X. find the analytic expression of function f (x)

F(X)-2F(1/X)=X (1)
Replace x with 1 / x, yes
F(1/X)-2F(X)=1/X (2)
(1)+2*(2):F(X)-4F(X)=X-2/X ==> F(X)=(1/3)(2/X-X)
F (x) domain x is not equal to 0

If f (x) satisfies f (1 / (1-x)) = 1 / 2F (x) + 1, then f (3) =?

F(3)=2
Let 1 / (1-x) be x, and the original formula is
F（X）=（1/2）F（1/（1—X））+1
F (x) = 2 is a constant reference function

Given f (x) = 2x + 2-x, if f (a) = 3, then f (2a)=______ ．

∵ f (a) = 3 = 2A + 2-A, ∵ f (2a) = 22a + 2-2a = (2a + 2-A) 2-2 = 32-2 = 7

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