# Function Notation In Math

in STEMGeeks28 days ago

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.

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## Topics

• Why f(x) Notation Instead of y =
• Substituting Number Values For x With Function Notation

## 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.

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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.

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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.

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