# 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.

greatness96 (69)4 years agoBeautiful 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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steemiteducation (72)4 years ago