f(x)=2f(1/x)=2x-1 eching

$$f ( x ) = 2 f ( \frac { 1 } { x } ) = 2 x - 1$$

f uchun yechish

$$f=x^{2}-\frac{x}{2}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$2f\times 1=2xx+x\left(-1\right)$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$2f\times 1=2x^{2}+x\left(-1\right)$$

2 hosil qilish uchun 2 va 1 ni ko'paytirish.

$$2f=2x^{2}+x\left(-1\right)$$

Tenglama standart shaklda.

$$2f=2x^{2}-x$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2f}{2}=\frac{x\left(2x-1\right)}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$f=\frac{x\left(2x-1\right)}{2}$$

x\left(-1+2x\right) ni 2 ga bo'lish.

$$f=x^{2}-\frac{x}{2}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{16f+1}+1}{4}\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{16f+1}+1}{4}\text{, }&f\neq 0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{16f+1}+1}{4}\text{, }&f\geq -\frac{1}{16}\\x=\frac{-\sqrt{16f+1}+1}{4}\text{, }&f\neq 0\text{ and }f\geq -\frac{1}{16}\end{matrix}\right,$$