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.

inverse functions

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 3Continue reading

Why the Area of a Rhombus is Half the Product of its Diagonals

A rhombus is a parallelogram with four congruent sides. Since it is a parallelogram, it has also all the properties of a parallelogram. One of these properties is that the diagonals bisect each other. That is, they divide each other into two equal parts.

Another property of a rhombus is that the diagonals are perpendicular. So, summarizing all the properties above, if we have rhombus ABCD, then,

\overline{AB} \cong \overline{BC} \cong \overline{CD} \cong \overline{DA}.

and

\overline{AC} \perp \overline{BD}. Continue reading

Math Expressions and Graphs in Google Docs with g(Math)

Last week, I wrote about a tutorial on how to create math expressions in a Google Forms using Latex. Embedding of Latex in Google Docs documents can be made using the new g(Math) Google Docs Add On. Although Google Docs has a built in equation editor, the addition of Latex through g(Math) can make embedding of more complicated equations possible.

In addition to Latex, you can also create graphs using g(Math). Once you have added this add on, you can create graphs using the side bar of your Google Docs window.

Watch John McGowan, creater of g(Math), demonstrates how to use g(Math) on Google Docs.

For those who are not familiar with Latex, it is a typesetting system used to create scientific documents. It can also be used to create complicated math expressions. You can read my introduction and brief tutorial about latex in case you don’t know about it.

 

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