Function NotationsteemCreated with Sketch.

in #mathematics4 years ago

Hi there. This post is an introduction to function notation from (high-school) mathematics.


Featured Image Source

When it comes to equations, the variable y is commonly used to represent the dependent variable with x being the independent variable. There are times when we deal with multiple equations such as:


Image Source

With those equations, when we substitute a value of 2 for x for example it is not entirely clear which y equation we put x = 2 into.

One solution is to use subscripts such as . A more common approach is the use of function notation such as f(x) and g(x). (You can combine subscripts and function notation too!)

Function notation makes it easier for the math reader to identify which equation is being used for the substitution. Instead of y, we would use use instead. (Different letters are used to indicate the functions are different.)

For the case of substituting x = 2, we have f(2) and g(2) as follows:


Image Source

As a summary, here is an informative image. The independent variable x is the input while y = f(x) is the output from x. Think of functions like a vending machine.


Image Source

Examples


For the first three examples we have h(x) = 10x + 3.


Example One

What is h(1)?

h(1) = 10(1) + 3 = 10 + 3 = 13

We have h(1) as 13.


Example Two

What is h(-2)?

h(-2) = 10(-2) + 3 = -20 + 3 = -17


Example Three

What is h(a) where a is some number?

In the previous examples, the variable x was replaced with a number. Here we do a similar procedure and substitute x with a.

h(a) = 10a + 3


Example Four

Function notation can be applied to more complex functions.


Example Five (Composition Functions)

This example is a little bit tougher. You can have functions inside functions.

Answer

When it comes to composition functions, you start with the inside. For f(g(2)), you evaluate g(2) first and use the value from g(2) into the function f.

With g(f(2)), f(2) is evaluated first and the value from that is put into the function g(x).

The answers are f(g(2)) = 8 and g(f(2)) = 11.


Math text and images are done in LaTeX with QuickLaTeX.com.


Image Source

Sort:  

Beautiful lecture, @dkmathstats. I remember my secondary school days. Simultaneous equations was my favourite. I hope I can teach it here, lol. @greatness96

Congratulations @dkmathstats, this post is the ninth most rewarded post (based on pending payouts) in the last 12 hours written by a User account holder (accounts that hold between 0.1 and 1.0 Mega Vests). The total number of posts by User account holders during this period was 2082 and the total pending payments to posts in this category was $2133.89. To see the full list of highest paid posts across all accounts categories, click here.

If you do not wish to receive these messages in future, please reply stop to this comment.