Réitigh f(x)=2f(1/x)=2x-1

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

Réitigh do f.

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

$$x\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi x.

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

Méadaigh x agus x chun x^{2} a fháil.

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

Méadaigh 2 agus 1 chun 2 a fháil.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi 2.

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

Má roinntear é faoi 2 cuirtear an iolrúchán faoi 2 ar ceal.

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

Roinn x\left(-1+2x\right) faoi 2.

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

Réitigh do x. (complex solution)

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

Réitigh do x.

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