Hi there. Here is a guide on function notation in mathematics. This concept kind of has applications but this concept is a part of the algebra toolbox for math students.

Some math images rendered with Quicklatex.com.

## Topics

- Why f(x) Notation Instead of y =
- Substituting Number Values For x With Function Notation
- Advanced Examples
- Adding & Subtracting Functions

## Why f(x) Notation Instead of y =

Suppose you have two equations that have y = to something. Let's say you have `y = x + 2`

and `y = 3x + 10`

. If you have to substitute `x = 1`

into y, which y equation do you choose? The first one or the second one?

This is where function notation and `f(x)`

comes in. We can rewrite the above equations as `f(x) = x + 2`

and `g(x) = 3x + 10`

. Instead of saying substitute `x = 1`

into the function `f(x)`

we can say obtain the value of `f(1)`

(pronounced f of 1).

Function notation is a compact and simplified way of substituting values of x in different equations and functions.

## Substituting Number Values For x With Function Notation

Let's take at some example of function notation with substituting numbers for x.

**Example One**

Let `f(x) = 5x - 7`

, what is the value of `f(10)`

?

Replace the variable `x`

with the number 10. Then apply order of operations to get the answer of 43 `(50 - 7)`

.

**Example Two**

What is the value of g(-2) if `g(x) = x^2 - 7`

?

**Example Three - Exponential Function**

Evaluate `h(3)`

if `h(x)`

is ten to the power of x.

## Advanced Examples

The idea of function notation is not super complicated but some examples can get a bit technical and algebra intensive. Here are a few tougher examples.

**Example One**

In `f(x) = 5x + 2`

, what is `f(2x)`

?

At first this looks confusing. What you have to do is replace the input `x`

with the new input of `2x`

.

**Example Two**

In `g(x) = 2x - 1`

, what is `g(x + 7)`

?

Replace `x`

with the new input of `x + 7`

. Afterwards use algebra techniques to expand and simplify.

## Adding & Subtracting Functions

This concept of adding and subtracting fractions is a natural extension of function notation. I could write another post dedicated to this but I have decided to put some stuff here.

You can combine adding & subtracting functions with evaluating them given a value of x.

**Example One**

If `f(x) = x - 7`

, what is the value of `f(1) - f(3)`

?

The value of `f(1)`

is negative 6 and the value of `f(3)`

is negative 4. When you compute `f(1) - f(3)`

it is `-6 - -4`

. The answer here is negative two.

**Example Two**

With `f(x) = 2x + 1`

and `g(x) = x - 3`

, what is the value of `f(1) + g(3)`

?

From the function `f(x)`

the value of `f(1)`

is 3. The value of `g(3)`

is 3 minus 3 which is equal to 0. Adding the values of `f(1)`

and `g(3)`

is 3 plus 0 which gives the answer of 0.

Posted using STEMGeeks

stemsocial (63)Notification 27 days ago