Since the image isn't visible, I'll assume a common problem of this type: Given (f(x) + 2f\left(\frac{1}{x}\right) = 3x), find (f(x)).

Step 1: Replace (x) with (\frac{1}{x})

Substitute (x \to \frac{1}{x}) in the original equation:
[f\left(\frac{1}{x}\right) + 2f(x) = \frac{3}{x}\quad \text{(Equation 2)}]

Step 2: Solve the system of equations

We have two equations:

1. (f(x) + 2f\left(\frac{1}{x}\right) = 3x)
2. (2f(x) + f\left(\frac{1}{x}\right) = \frac{3}{x})

Multiply Equation 2 by 2:
[4f(x) + 2f\left(\frac{1}{x}\right) = \frac{6}{x}\quad \text{(Equation 3)}]

Subtract Equation 1 from Equation 3:
[3f(x) = \frac{6}{x} - 3x]

Divide both sides by 3:
[f(x) = \frac{2}{x} - x]

Answer: (\boxed{f(x) = \frac{2}{x} - x}) or (\boxed{\frac{2 - x^2}{x}}) (both are equivalent).

If the problem differs, please provide more details, but this is a typical solution for such functional equations.

(\boxed{\frac{2}{x} - x})

作者声明:本文包含人工智能生成内容。