Whakaoti i te {l}{f{(x)}=-6x+3}{g{(x)}=3x+21x^-3}{h=f{(-3)}}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { f {(x)} = -6 x + 3 }\\ { g {(x)} = 3 x + 21 x ^ {-3} }\\ { h = f {(-3)} }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Whakaoti mō f, x, g, h

$$x=\frac{162}{325}+\frac{9}{325}i\approx 0.498461538+0.027692308i$$

$$f=-\frac{1}{3}i\approx -0.333333333i$$

$$g=\frac{727792}{2187}-\frac{18088}{243}i\approx 332.780978509-74.436213992i$$

$$h=i$$

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.

$$i=f\left(-3\right)$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{i}{-3}=f$$

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

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

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

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

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

$$-\frac{1}{3}ix=-6x+3$$

Me tāpiri te 6x ki ngā taha e rua.

$$-\frac{1}{3}ix+6x=3$$

Pahekotia te -\frac{1}{3}ix me 6x, ka \left(6-\frac{1}{3}i\right)x.

$$\left(6-\frac{1}{3}i\right)x=3$$

Whakawehea ngā taha e rua ki te 6-\frac{1}{3}i.

$$x=\frac{3}{6-\frac{1}{3}i}$$

Me whakarea te taurunga me te tauraro o \frac{3}{6-\frac{1}{3}i} ki te haumi hiato o te tauraro, 6+\frac{1}{3}i.

$$x=\frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}$$

Mahia ngā whakarea i roto o \frac{3\left(6+\frac{1}{3}i\right)}{\left(6-\frac{1}{3}i\right)\left(6+\frac{1}{3}i\right)}.

$$x=\frac{18+i}{\frac{325}{9}}$$

Whakawehea te 18+i ki te \frac{325}{9}, kia riro ko \frac{162}{325}+\frac{9}{325}i.

$$x=\frac{162}{325}+\frac{9}{325}i$$

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

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=3\left(\frac{162}{325}+\frac{9}{325}i\right)+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Whakareatia te 3 ki te \frac{162}{325}+\frac{9}{325}i, ka \frac{486}{325}+\frac{27}{325}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{162}{325}+\frac{9}{325}i\right)^{-3}$$

Tātaihia te \frac{162}{325}+\frac{9}{325}i mā te pū o -3, kia riro ko \frac{214}{27}-\frac{971}{729}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+21\left(\frac{214}{27}-\frac{971}{729}i\right)$$

Whakareatia te 21 ki te \frac{214}{27}-\frac{971}{729}i, ka \frac{1498}{9}-\frac{6797}{243}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{486}{325}+\frac{27}{325}i+\left(\frac{1498}{9}-\frac{6797}{243}i\right)$$

Tāpirihia te \frac{486}{325}+\frac{27}{325}i ki te \frac{1498}{9}-\frac{6797}{243}i, ka \frac{491224}{2925}-\frac{2202464}{78975}i.

$$g\left(\frac{162}{325}+\frac{9}{325}i\right)=\frac{491224}{2925}-\frac{2202464}{78975}i$$

Whakawehea ngā taha e rua ki te \frac{162}{325}+\frac{9}{325}i.

$$g=\frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i}$$

Me whakarea te taurunga me te tauraro o \frac{\frac{491224}{2925}-\frac{2202464}{78975}i}{\frac{162}{325}+\frac{9}{325}i} ki te haumi hiato o te tauraro, \frac{162}{325}-\frac{9}{325}i.

$$g=\frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}$$

Mahia ngā whakarea i roto o \frac{\left(\frac{491224}{2925}-\frac{2202464}{78975}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}{\left(\frac{162}{325}+\frac{9}{325}i\right)\left(\frac{162}{325}-\frac{9}{325}i\right)}.

$$g=\frac{\frac{55984}{675}-\frac{18088}{975}i}{\frac{81}{325}}$$

Whakawehea te \frac{55984}{675}-\frac{18088}{975}i ki te \frac{81}{325}, kia riro ko \frac{727792}{2187}-\frac{18088}{243}i.

$$g=\frac{727792}{2187}-\frac{18088}{243}i$$

Kua oti te pūnaha te whakatau.

$$f=-\frac{1}{3}i x=\frac{162}{325}+\frac{9}{325}i g=\frac{727792}{2187}-\frac{18088}{243}i h=i$$