When x ≥ 0, f (x) = - x + 1, then the analytic expression of F (x) is______ ．

When x ≥ 0, f (x) = - x + 1, then the analytic expression of F (x) is______ ．

Let x ＜ 0, then - x ＞ 0, and f (x) = f (- x) = - (- x) + 1 = x + 1, then the analytic expression of function f (x) on the domain R is: F (x) = − x + 1 x ≥ 0 x + 1 x ＜ 0, so the answer is: F (x) = − x + 1 x ≥ 0 x + 1 x ＜ 0

If f (x) satisfies the relation f (x) + 2F (1 / x) = 3x, find f (x). Substitute 1 / x into f (x) + 2F (1 / x) = 3x, (1)
Find the analytic expression of the following functions
If f (x) satisfies the relation f (x) + 2F (1 / x) = 3x, find f (x)
Substituting 1 / x into
f(x)+2f(1/x)=3x,(1)
We get f (1 / x) + 2F (x) = 3 / X (2)
Then (2) X2 - (1) was added into the matrix
f(x)=2/x-x
I just don't know how to subtract one from X2, and how to get the result in the end?

That is to multiply both ends of formula (2) by 2, and then subtract from formula (1), which can eliminate f (1 / x),
It is equivalent to using the method of addition, subtraction and elimination to solve the system of linear equations of two variables (regarding f (x) as an unknown number and f (1 / x) as another unknown number)

If the function f (x) satisfies the relation f (x) + 2F (1 / x) = 3x, then the value of F (2) is ()

Let x = 2. F (2) + 2F (1 / 2) = 6
Let x = 1 / 2 F (1 / 2) + 2F (2) = 3 / 2
The solution is f (2) = - 1
f(1/2)=7/2