Whakaoti i te {l}{f{(x)}=-4x-4}{g=f{(-1/5)}}{h=g}{i=h}{j=i}{k=j}{l=k}{m=l}{n=m}{o=n}{p=o}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { f {(x)} = -4 x - 4 }\\ { g = f {(-\frac{1}{5})} }\\ { h = g }\\ { i = h }\\ { j = i }\\ { k = j }\\ { l = k }\\ { m = l }\\ { n = m }\\ { o = n }\\ { p = o }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

Whakaoti mō f, x, g, h, j, k, l, m, n, o, p, q, r

$$r=i$$

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.

$$i=f\left(-\frac{1}{5}\right)$$

Me whakarea ngā taha e rua ki te -5, te tau utu o -\frac{1}{5}.

$$-5i=f$$

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

$$f=-5i$$

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

$$-5ix=-4x-4$$

Me tāpiri te 4x ki ngā taha e rua.

$$-5ix+4x=-4$$

Pahekotia te -5ix me 4x, ka \left(4-5i\right)x.

$$\left(4-5i\right)x=-4$$

Whakawehea ngā taha e rua ki te 4-5i.

$$x=\frac{-4}{4-5i}$$

Me whakarea te taurunga me te tauraro o \frac{-4}{4-5i} ki te haumi hiato o te tauraro, 4+5i.

$$x=\frac{-4\left(4+5i\right)}{\left(4-5i\right)\left(4+5i\right)}$$

Mahia ngā whakarea i roto o \frac{-4\left(4+5i\right)}{\left(4-5i\right)\left(4+5i\right)}.

$$x=\frac{-16-20i}{41}$$

Whakawehea te -16-20i ki te 41, kia riro ko -\frac{16}{41}-\frac{20}{41}i.

$$x=-\frac{16}{41}-\frac{20}{41}i$$

Kua oti te pūnaha te whakatau.

$$f=-5i x=-\frac{16}{41}-\frac{20}{41}i g=i h=i j=i k=i l=i m=i n=i o=i p=i q=i r=i$$