For the following exercises, find the inverse of the function with the domain given. $f(x)=\sqrt{4 x+5}-3$

For the following exercises, sketch the graph of the indicated function. $g(x)=\log (6-3 x)+1$

Use a calculator to check any three of your answers in Exercises 79-90.

For the following exercises, simplify each expression.\

$$\frac{4 \sqrt{2 n}}{\sqrt{16 m^4}}$$

For the following exercises, simplify the expression.\

$$\frac{a}{2^7}(64)-12 a \div 6$$

Solve the exercises below and write the correct answer.

$2 x-\frac{1}{2}=4-3 x$

In this exercises, $c^2=a^2+b^2$.

In the right triangle, find $a$ if $b=a+3$ and $c=a+4$.

For the following exercises, simplify the expression. $9(y+2) \div 3 \cdot 2+1$

In Exercises, find the first derivative of the algebraic function.

$y=\sqrt[3]{9 x^2+4}$

Without graphing, find the vertex of the parabola that is the graph of the given function.

f(x) = 3x$^2$-12x+5

For the following exercises, find the x- or t-intercepts of the polynomial functions. $f(x)=x^{3}+6 x^{2}-7 x$

For the following exercises, simplify each expression.\

$$\frac{\sqrt{8}}{1-\sqrt{3 x}}$$

For the following exercises, simplify the expression.\

$$4 \cdot 3+18 x \div 9-12$$

A regular octagon is rotated about a centrally located point (as shown). How many rotations are needed to repeat the given octagon vertex for vertex, if the angle of rotation is

a) $10^{\circ}$ ?

b) $45^{\circ}$ ?

c) $90^{\circ}$ ?

d) $120^{\circ}$ ?