Whakaoti i te {l}{f{(x)}=3x-1}{g=f{(-2)}}{h=g}{i=h}{j=i}{k=j}{l=k}{m=l}{text{Solvefor}ntext{where}}{n=m}

$$\left. \begin{array} { l } { f {(x)} = 3 x - 1 }\\ { g = f {(-2)} }\\ { h = g }\\ { i = h }\\ { j = i }\\ { k = j }\\ { l = k }\\ { m = l }\\ { \text{Solve for } n \text{ where} } \\ { n = m } \end{array} \right.$$

Whakaoti mō f, x, g, h, j, k, l, m, n

$$n=i$$

Ngā Upane Otinga

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

$$h=i$$

Whakaarohia te whārite tuatoru. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$i=g$$

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

$$g=i$$

Whakaarohia te whārite tuarua. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$i=f\left(-2\right)$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{i}{-2}=f$$

Whakawehea te i ki te -2, kia riro ko -\frac{1}{2}i.

$$-\frac{1}{2}i=f$$

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

$$f=-\frac{1}{2}i$$

Whakaarohia te whārite tuatahi. Me kōkuhu ngā uara tāupe mōhiotia ki te whārite.

$$-\frac{1}{2}ix=3x-1$$

Tangohia te 3x mai i ngā taha e rua.

$$-\frac{1}{2}ix-3x=-1$$

Pahekotia te -\frac{1}{2}ix me -3x, ka \left(-3-\frac{1}{2}i\right)x.

$$\left(-3-\frac{1}{2}i\right)x=-1$$

Whakawehea ngā taha e rua ki te -3-\frac{1}{2}i.

$$x=\frac{-1}{-3-\frac{1}{2}i}$$

Me whakarea te taurunga me te tauraro o \frac{-1}{-3-\frac{1}{2}i} ki te haumi hiato o te tauraro, -3+\frac{1}{2}i.

$$x=\frac{-\left(-3+\frac{1}{2}i\right)}{\left(-3-\frac{1}{2}i\right)\left(-3+\frac{1}{2}i\right)}$$

Mahia ngā whakarea i roto o \frac{-\left(-3+\frac{1}{2}i\right)}{\left(-3-\frac{1}{2}i\right)\left(-3+\frac{1}{2}i\right)}.

$$x=\frac{3-\frac{1}{2}i}{\frac{37}{4}}$$

Whakawehea te 3-\frac{1}{2}i ki te \frac{37}{4}, kia riro ko \frac{12}{37}-\frac{2}{37}i.

$$x=\frac{12}{37}-\frac{2}{37}i$$

Kua oti te pūnaha te whakatau.

$$f=-\frac{1}{2}i x=\frac{12}{37}-\frac{2}{37}i g=i h=i j=i k=i l=i m=i n=i$$