Find $(f \cdot g)(-2)$ for the following functions.

$$\begin{array}{l}{f(x)=-x^{2}+2 x-2} \\ {g(x)=2 x+3}\end{array}$$

A. -20 B. 8 C. 120 D. 215

Use elimination to solve each system of equations.

$$\left\{\begin{array}{l}2 x-y-3 z=1 \\ 4 x+3 y+2 z=-4 \\ -3 x+2 y+5 z=-3\end{array}\right.$$

In this problem, find all eigenvalues and eigenvectors of the given matrix.

$$\left(\begin{array}{lll}3 & 2 & 4 \\ 2 & 0 & 2 \\ 4 & 2 & 3\end{array}\right)$$

Find the solution of the system. If necessary, round answers to the nearest tenth.

$$\begin{array}{l}{y=-\frac{7}{3} x+\frac{16}{3}} \\ {y=\frac{4}{3} x+\frac{38}{3}}\end{array}$$

Perform the row operations indicated beside each matrix. Write the matrix obtained.

$$\left[\begin{array}{rrr|r}{1} & {3} & {2} & {-4} \\ {2} & {-1} & {3} & {5} \\ {4} & {6} & {-2} & {3}\end{array}\right]$$

$$\begin{array}{l}{-2 \mathrm{R} 1+\mathrm{R} 2 \rightarrow \mathrm{R} 2} \\ {-4 \mathrm{R} 1+\mathrm{R} 3 \rightarrow \mathrm{R} 3}\end{array}$$

Tell which factorization is correct.

$$\left. \begin{array} { l } { 4 x ^ { 2 } - 4 x - 15 } \\ { ( 2 x - 5 ) ( 2 x + 3 ) \text { or } ( 4 x + 5 ) ( x - 3 ) } \end{array} \right.$$

Let

$$F _ { 1 } \left( y _ { 1 } \right) \text { and } F _ { 2 } \left( y _ { 2 } \right)$$

be two distribution functions. For any

$$\alpha , - 1 \leq \alpha \leq 1$$

, consider

$$Y _ { 1 }$$

and

$$Y _ { 2 }$$

with joint distribution function

$$F \left( y _ { 1 } , y _ { 2 } \right) = F _ { 1 } \left( y _ { 1 } \right) F _ { 2 } \left( y _ { 2 } \right) \left[ 1 - \alpha \left\{ 1 - F _ { 1 } \left( y _ { 1 } \right) \right\} \left\{ 1 - F _ { 2 } \left( y _ { 2 } \right) \right\} \right]$$

. What is

$$F \left( y _ { 1 } , \infty \right)$$

, the marginal distribution function of

$$Y _ { 1 }$$

? [Hint: What is

$$F _ { 2 } ( \infty )$$

?]

describe how to transform the graph of y =ln x into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.

$$f(x)=ln(2-x)$$

Let us consider the following equation which is given by

$$f(x)=\left\{\begin{array}{rr} x-1, & x \leq 3 \\ 3 x-7, & x>3 \end{array}\right.$$

Find $\lim _{x \rightarrow 3^{-}} f(x)$.

Determine whether the given matrix is invertible.

$$\left[\begin{array}{rrr}{-1} & {0} & {0} \\ {0} & {2} & {0} \\ {0} & {0} & {\frac{1}{3}}\end{array}\right]$$

Find $\mathcal{L}\{f(t)\}$ for the function $f$ defined below.

$$f(t)=\left\{\begin{array}{ll}{t,} & {0<t<3} \\ {3,} & {t>3}\end{array}\right.$$

Consider $A$ be the given matrix

$$\left[\begin{array}{rr} 1 & -1 \\ -2 & 3 \end{array}\right]$$

Now calculate the given quantity.

(e) $p(A)$, where $p(x)=2 x^2-x+1$

Identify the element specified for the following matrix.

$$\begin{bmatrix}-2 & 0 & 2 & 4\\3 & 1 & 5 & -1\\1 & 4 & -1 & 3\end{bmatrix}$$

$$a_{32}$$

Sketch a graph of the piecewise defined function.

$$f ( x ) = \left\{ \begin{array} { l l } { - x } & { \text { if } x \leq 0 } \\ { 9 - x ^ { 2 } } & { \text { if } 0 < x \leq 3 } \\ { x - 3 } & { \text { if } x > 3 } \end{array} \right.$$