Functions

A function is an equation which consists of variables. The most basic functions consists only of one variable and usually we will denote this by x. A basic example would be f(x) = 2x -3. We denote function by f, if we have more than one function we usually make use of g and h and so forth.

f(x) means that we take the function f over the variable x. If for instance we want to calculate f(2) this means that we would replace every x in our equation with 2. In our example this would be f(2) = 2(2)-3 = 1. This equation is also called a linear equation, which will be explained in a future post.

Functions can also be combined, we can add, subtract, multiply and divide functions (given that the denominator is not zero in the case of division). Another type of combining function is called composite functions. That is when we take a function of a function, for example f(g(x)). Let's define g(x) = 3x². Then

f(g(x)) = f(3x²) = 2(3x²)-3 = 6x²-3. Now we have a new function which we created out of two other functions.

There are also inverse functions, see Inverses. It is easy to illustrate with composite functions. Since
f(g(x)) = 6x²-3

f ^-1­­(6x²-3) = 3x² and g ^-1­­(3x²) = x.

Functions are very useful in all fields of mathematics and almost everything in our world can be expressed by some equation or function.