
Inverse Function
y=4x5
Inverse function
y = 4x  5
Change x as y and y as x,
x = 4y  5
Write the y as function of x.
4y = x + 5
y = (x + 5)/4
f^1(x) = (x + 5)/4
Graph
Domain and Range
y = 4x  5
Domain: Set of all real numbers
Range: Set of all real

Density and Distribution Functions : Cauchy Density Function and Joint Distribution
Hence the variance of Y doesn't exist as well since .
Given a supply of U(0,1) values, how to simulate Y=tan(X)?
If X follows U(0,1), a uniform distribution over (0,1), then will follows . Hence, will follow .

34 Function Problems : Graphing, Translation, Reflection, Domains, Limits, Derivatives and Tangents
1) Y=2^x, y=e^x, y=5^x, y=20^x
2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x
_______________________________________________________________________
Make a sketch of the function.
7) y=4^x3
8) y=2x^x
9) y=3e^x
13) Starting with the graph

Basic slope intercept equations
x + y = 9
A) y is a function of x
B) y is not a function of x
7. Determine whether the equation defines y as a function of x.
x2 + y2 = 1
A) y is a function of x
B) y is not a function of x
8.

Coding in Matlab  Dot, cross, and triple products
Hence, assuming the input vectors are column vectors, we may define the scaler triple product as
function tri = triple_prod(x,y,z)
tri = det([x,y,z]);
Here, [x,y,z] forms a matrix with columns x,y,z.

Mathematics  Algebra
For the given function, these values occur at x = {2, 2}.
As x takes on very large positive values or very large negative values, y approaches the value x. This is seen by the fact that the function has a slant asymptote y = x.

Functions domains and range
The function f is defined as follows
f(x) = {4+2x if x<0
{x^2 if x>0
a) Find the domain of the function
b) Locate any intercepts
c) Graph function
d) Based on graph find range
e) Is f continuous on its domain?

The inverse of a function
Observe that if we consider f as a function from the set of nonnegative real numbers to the set of nonnegative real numbers, then it has an inverse y=√x.

Finding the domain and range of discontinuous functions
A step function is another example of a piecewise function though not a continuous function.
Step Function
This piecewise function is known as a step function.

Working with a sinusoidal function
The period of the function y = sin Ax is 2pi/A.
Note that A =  A 
The function's value must remain invariant as we use x in it. The smallest value of x for which the function is invariant is the period.