Whakaoti i te f^-1(x)=3x

$$f ^ { - 1 } ( x ) = 3 x$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&f=\frac{1}{3}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 3x mai i ngā taha e rua.

$$f^{-1}x-3x=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-3x+\frac{1}{f}x=0$$

Whakareatia ngā taha e rua o te whārite ki te f.

$$-3xf+1x=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-3fx+x=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-3f+1\right)x=0$$

He hanga arowhānui tō te whārite.

$$\left(1-3f\right)x=0$$

Whakawehe 0 ki te 1-3f.

$$x=0$$

Whakaoti mō f

$$\left\{\begin{matrix}\\f=\frac{1}{3}\approx 0.333333333\text{, }&\text{unconditionally}\\f\neq 0\text{, }&x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakaraupapatia anō ngā kīanga tau.

$$\frac{1}{f}x=3x$$

Tē taea kia ōrite te tāupe f ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te f.

$$1x=3xf$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3xf=1x$$

Whakaraupapatia anō ngā kīanga tau.

$$3fx=x$$

He hanga arowhānui tō te whārite.

$$3xf=x$$

Whakawehea ngā taha e rua ki te 3x.

$$\frac{3xf}{3x}=\frac{x}{3x}$$

Mā te whakawehe ki te 3x ka wetekia te whakareanga ki te 3x.

$$f=\frac{x}{3x}$$

Whakawehe x ki te 3x.

$$f=\frac{1}{3}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=0\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&f=\frac{1}{3}\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 3x mai i ngā taha e rua.

$$f^{-1}x-3x=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-3x+\frac{1}{f}x=0$$

Whakareatia ngā taha e rua o te whārite ki te f.

$$-3xf+1x=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-3fx+x=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-3f+1\right)x=0$$

He hanga arowhānui tō te whārite.

$$\left(1-3f\right)x=0$$

Whakawehe 0 ki te 1-3f.

$$x=0$$