\( \left. \begin{array} { l } { \frac { 2 | x - 2 | } { 4 } = \frac { \sqrt { 8 \cdot 4 ^ { | x | } - 2 | } } { 2 ^ { | x - 2 | } } } \end{array} \right. \)

Chùng minh đàng thức: \( (\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})+\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}-5 \sqrt{\frac{1}{5}}=2 \)

Expand \( \frac{n}{2}(4+(n-1) \times 2) \)

13) If \( f(x)=\frac{x-1}{x-4} \) and \( f^{-1}(x) \) is the inverse of \( f \), what is the value of \( f^{-1}(4) ? \) \( \begin{array}{llll}\text { (A) } 5 & \text { (B) } 6 & \text { (C) } 8 & \text { (D) } 10 \\ \text { a } & \\ \text { b } & \end{array} \)

\( \begin{array}{ll}\text { 2. } & 2 \cdot \mathrm{C}_{0}+3 \cdot \mathrm{C}_{1}+4 \cdot \mathrm{C}_{2}+\ldots+(\mathrm{n}+2) \cdot \mathrm{C}_{\mathrm{n}}=(\mathrm{n}+4) \cdot 2^{\mathrm{n}-1} \\ \text { 3. } & 2 \cdot \mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+8 \cdot \mathrm{C}_{2}+\ldots(\mathrm{n}+1) \text { terms }=(3 \mathrm{n}+4) \cdot 2^{\mathrm{n}-1} \\ \text { 4. } & 3 \cdot \mathrm{C}_{1}+7 \cdot \mathrm{C}_{2}+11 \cdot \mathrm{C}_{3}+\ldots \mathrm{n} \text { terms }=1+(2 \mathrm{n}-1) 2^{\mathrm{n}} \\ \text { 5. } & 7 \mathrm{C}_{1}-12 \cdot \mathrm{C}_{2}+\ldots(-1)^{\mathrm{n}-1} \cdot(5 \mathrm{n}+2) \mathrm{C}_{\mathrm{n}}=2\end{array} \)

Ex. (8): Find the new form of the equation of the curve Fig \( (7 \) \[ x^{2}+3 x y-y^{2}-x+5 y-6=0 \] When shifting axes at the point \( (-1,1) \) without change of direction. \[ (\alpha, \beta) \]