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The elimination method of solving function in senior one If f (x) satisfies the equation AF (x) + F (1 / x) = ax, X ∈ R, X ≠ 0, a is a constant, a ≠± 1, then f (x)=__ Solution: using the elimination method ∵ AF (x) + F (1 / x) = ax If x is replaced by 1 / x, then 1 / X is replaced by X The following is omitted I just want to ask why it can be converted That's not waiting After the transformation, a system of equations is formed with the first equation. I'll try again. It can't be solved at all. I'm looking for advice from experts.
The premise of conversion is that x, 1 / X are all in the domain,
This is explained by AF (x) + F (1 / x) = ax itself
Function holds for all values in the domain, so x and 1 / X are brought into the original formula, and the original formula holds,
In addition, we should understand that x is just a symbol, a form, which represents all the values in the domain
For example, it can represent 2 or 1 / 2
After the conversion, it became
af(1/x)+f(x)=a/x （1）
A = 0 is simpler,
When a is not equal to 0
Equation (1) divide both sides by a at the same time
We can find f (x)
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