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1. If \( f(x)=7 x+12 \) and \( f(x(x))=21 x^{2}+40 \) Find \( g(4) \) A) 40 B) \( \$ 2 \) C) 40 D) 50

1. (10 points) Compute the product \( C \cdot\left(A^{T}+B\right) \) where \[ A=\left(\begin{array}{cc}-2 & 3 \\ 4 & -5 \\ 1 & 0\end{array}\right), B=\left(\begin{array}{ccc}4 & -7 & 1 \\ -5 & 6 & 2\end{array}\right), \quad C=\left(\begin{array}{cc}1 & 2 \\ 2 & 1 \\ 3 & 3\end{array}\right) \]

№ 1. Даны векторы \( \vec{a}=(3 ;-5 ; 1), \vec{b}=(6 ; 2 ;-2) \) 1. Найти координаты векторов: \( -2 \vec{a}, \vec{a}+\vec{b}, \vec{a}-\vec{b} \) 2. Построить векторы: \( \vec{a}, \vec{b},-2 \vec{a}, \vec{a}+\vec{b}, \vec{a}-\vec{b} \) 3. Найти длину векторов: \( |\vec{a}|,|\vec{b}|,|-2 \vec{a}|,|\vec{a}+\vec{b}|,|\vec{a}-\vec{b}| \) № 2.

Given: \( f(x)=a^{x}-1 \) for \( a>0, \mathrm{~B}\left(2 ; \frac{-5}{9}\right) \) is a point on \( f \). 4.1 Walculate the value of \( a \). 4.3 Sketch the graph of \( f \). Clearly show the intercepts with the axes and asymptote if any. 4.4 It is further given that C is a point on \( f \) at \( y=\frac{19}{8} \). Determine the coordinates of \( \mathrm{C}^{\prime} \), the image of C , when C is reflected about the lin \( y=x \).

3. Differentiate between strict stationarity and weak stationarity (4Marks)