Find the domain of the function $$f\left(x\right)=\frac{x+3}{2x-3}$$

Find the domain and the range of the function $$f\left(x\right)=\frac{{\sqrt[\,]{3x-6}}}{x^{2}-6x+5}$$

Let $f\left(x\right)={\sqrt[3]{x}}$, and  $g\left(x\right)=x^{2}+x-2$. Find $\left(f\circ g\right)\left(x\right)$ and $\left(g\circ f\right)\left(x\right)$.

Given $f\left(x\right)=x+7$, write a formula for the function obtained by shifting $f\left(x\right)$ up $14$ units and left $14$ units.

Solve $$\left|2x-3\right|=5$$

Assume that $f$ is a one-to-one function, and $f(2)=4$, $f(5)=-1$. What are the input and output values for the inverse function, $f^{-1}$?

Enter the input values in ascending order and output values as they correspond to the input values.

Determine the $x-$intercepts and $y-$intercepts of $$y=x^{5}\VMinusc x^{3}\VPlusd x\,$$

Which of the following are graphs of polynomial functions?

A)      B)

C)      D)

Are $f(x)=\frac{1}{x-4}$ and $g(x)=\frac{1}{x}+4$  inverses of each other for $x\neq 0, 4$?

Use the quotient rule for logarithms to fully expand this logarithmic expression.
$$\ln\left(\frac{\frac{14}{y}}{\frac{x}{5}}\div \frac{\frac{2}{x}}{\frac{y}{7}}\right)$$

The intensity $I$, can be modelled by the equation $I=10^{1\VMinusa x}$ where $x$ is depth in meters. Determine the depth when $I=\Vb $. 

A foreman is supervising an electrician repairing a power line at the top of a pole. The foreman, who is $1.8\,\um$ tall, is standing $7.5\um$ away from the pole. The foreman needs to tilt their head back $$60^{\circ}$$ to see the electrician. How high from the ground is the electrician?

For the following angle $\theta$, determine the values of $\cos,\sin,\tan$. Round to two decimal points.

Find $\theta$. Give your answer in radians.

Given $\alpha=82^\circ$, $\gamma = 50^\circ$, and $b=10$, find the remaining sides and angles. Round them to two decimal points.

Two planes leave the same airport at the same time. The first plane travels at $800\ukm/\uhr$ in one direction, and the second plane travels at $700\ukm/\uhr$ in another direction. After an hour and a half, the planes are $2100\ukm $ apart. What is the angle between the two planes? Round your final answer to two decimal places.

A group of people are going shopping at a mall together. A family purchases $5$ t-shirts, $1$ cap, and $2$ dresses, and the total is $\$198$. A couple buys $3$ t-shirts, $2$ caps, and $1$ dress, and spends $\$131$. Another couple buys $2$ t-shirts, $1$ cap and $1$ dress, and spends $\$93$. What is the cost of each item?

Let $x$ be the cost of a t-shirt, $y$ be the cost of a cap, and $z$ be the cost of a dress.

Identify if the image of a parabola follows the equation $y^2=4px$  or  $x^2=4py$.  Then, find the directrix, focus, and the endpoints of the latus rectum of the parabola below.

Write a recursive formula for the geometric sequence below.
$$\left\{5,2,\frac{4}{5},\frac{8}{25},\dots\right\}$$

Find the sum of the arithmetic series below.
$$\sum_{k=1}^{10}\left(2k-1\right)$$

One card is drawn from a full deck. What is the probability of drawing a black card or a face card (one of jack, queen, or king)?