شاه کلید نکات
شاه کلید سوال
۱ با توجه به ضابطهٔ \(f_1(x) = x + 1\) و \(f_2(x) = x - 1\) درخت زیر را به ازای x = 2 کامل کنید.
\(\begin{array}{l}{f_1}(2) = 2 + 1 = 3\\\\{f_2}(2) = 2 - 1 = 1\\\\{f_3}(2) = {f_1}(2) + {f_2}(2) = 3 + 1 = 4\\\\{f_4}(2) = {f_1}(2) - {f_2}(2) = 3 - 1 = 2\\\\{f_5}(2) = {f_2}(2) - {f_1}(2) = 1 - 3 = - 2\\\\{f_6}(2) = {f_1}(2) \times {f_2}(2) = 3 \times 1 = 3\\\\{f_7}(2) = \frac{{{f_1}(2)}}{{{f_2}(2)}} = \frac{3}{1} = 3\\\\{f_8}(2) = \frac{{{f_2}(2)}}{{{f_1}(2)}} = \frac{1}{3}\\\\{f_9}(2) = \frac{{{f_3}(2)}}{{{f_5}(2)}} = \frac{4}{{ - 2}} = - 2\\\\{f_{10}}(2) = {f_4}(2) \times {f_6}(2) = 2 \times 3 = 6\\\\{f_{11}}(2) = {f_7}(2) + {f_8}(2) = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{{10}}{3}\\\\{f_{12}}(2) = {f_{10}}(2) \times {f_{11}}(2) = 6 \times \frac{{10}}{3} = 20\\\\{f_{13}}(2) = {f_9}(2) \times {f_{12}}(2) = - 2 \times 20 = - 40\end{array}\)
۲ اگر \(f = \{(-1, 3) \text{ و } (4, -1) \text{ و } (2, 0)\}\) و \(g = \{(-1, 2) \text{ و } (3, -1) \text{ و } (2, 5)\}\) باشد، توابع زیر را مشخص کنید.
\(\begin{array}{l}f + g = \\\\f \times g = \\\\\frac{g}{f} = \\\\\frac{f}{g} = \\\\f - g = \\\\g - f = \end{array}\)
\(\begin{array}{l}{D_{f \cap g}} = \{ 2, - 1\} = {D_{f + g}} = {D_{f - g}} = {D_{g - f}}\\\\f + g = \{ (2,5),( - 1,5)\} \\\\{D_{f \times g}} = \{ 2, - 1\} \\\\f \times g = \{ (2,0),( - 1,6)\} \\\\{D_{\frac{g}{f}}} = \{ - 1\} \\\\\frac{g}{f} = \{ ( - 1,\frac{2}{3})\} \\\\{D_{\frac{f}{g}}} = \{ 2, - 1\} \\\\\frac{f}{g} = \{ (2,0),( - 1,\frac{3}{2})\} \\\\f - g = \{ (2, - 5),( - 1,1)\} \\\\g - f = \{ (2,5),( - 1, - 1)\} \end{array}\)
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