## Revisiting Khan Academy After Four Years

It was four years ago when I discovered Khan Academy, which as far as I can remember a Youtube channel with more than a thousand videos. If I am not mistaken, it was only then managed by Salman Khan, it’s founder.

A year ago or two, when I searched the internet, I learned that Khan Academy has already its own website and it is run already by a group of educators. Three weeks ago, I started using the website. As of this writing, I have already watched 29 videos (oh yes, I watched them from start to end) and earned 56,340 points. 🙂  » Read more

## Understanding the Concept of Inverse Functions

Let us consider the functions

$f(x) = x^3$  and $g(x) = \sqrt[3]{x}$.

The table on the left shows the ordered pairs $(x,f(x))$. We used $f(x)$ and substitute them to $x$ in the second table.

As we can see, all the values of $g(x)$ are the same as those of $x$ in the first table. For example,  if we have $x = 3$ in the first table, applying $f$, we get  27 as output. On the other hand, if we apply $g$ to 27, the value returns to $3$» Read more

## How to Use the Factorial Notation

We have had several discussions about the factorial notation, so I think this introduction is a bit late. However, it is important that you know these basic facts in order to perform calculations and understand better in later discussions.

The factorial of a non-negative integer $n$ is the product of all the positive numbers less than $n$. For example, the

$4! = 4 \times 3 \times 2 \times 1 = 24$.

and

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$.

In Introduction to Permutations, we have discussed that there are $n!$ ways to arrange $n$ distinct objects into a sequence. For instance, if we have 3 objects namely A, B, and C, then they can be arranged in $3! = 3 \times 2 \times 1 = 6$ ways. The arrangement are as follows:

$ABC, ACB, BAC, BCA, CAB, CBA$.

We have also learned some reasons why mathematicians chose the definition $0! = 1$. » Read more

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