Function Notation
Hi there. This post is an introduction to function notation from (high-school) mathematics.
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:
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:
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.
Examples
For the first three examples we have h(x) = 10x + 3.
Example One
What is h(1)?
We have h(1) as 13.
Example Two
What is h(-2)?
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
.
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.
Beautiful lecture, @dkmathstats. I remember my secondary school days. Simultaneous equations was my favourite. I hope I can teach it here, lol. @greatness96
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