# Function NotationsteemCreated with Sketch.

in #mathematics4 years ago

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

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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:

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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:

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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.

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### 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.

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.

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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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