What Is A Mathematical Functions?

By Author: nandan nayak
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Mathematical functions are the way to express any expression with a potential input and a potential output. It works like a machine, which means the way we put the input, we get the output.
For example: -
F (x) = x^3
In this expression ‘F’ is the name of the function,’(x)’ is the input and x^3 is the output. If we input x = 2 we get f(2) = 2^3 = 8 and if we put x = 3, we get f(x) = 3^3 = 9. So the output depends on the input we put. The output changes with respect to the value of the input.
The input of the function is called the ‘argument’ and the output of the function is called the ‘value’.
Following are the examples of some Math Function or Functions Math: -
Y = 3x + 5
M = 6n^2 – 5n + 8
Z = y^3 – 3y
Functions
A function contains the input and the output. The output is related to the input we put. A function is usually written as: -
Suppose, f(x) = x^2
This means f is a function of x, whatever we put in the function ‘x’ and it is the input. The output changes with respect to the value of ‘x’. For the example above f(3) = ...
... 3^2 = 9.
Some examples of functions are: -
x^2 + 4
y – 7
x^3 + x^2 + 3
Combining functions
There are five ways of combining two functions: -
1. Addition: By adding the values of f and g, we get a new function ‘f+g’ such as f(x) + g(x) = (f+g) (x)
2. Subtraction: By subtracting values of ‘g’ from ‘f’, we get a new function ‘f-g’, such as f(x) – g(x) = (f-g) (x)
3. Multiplication: By multiplying values of ‘f’ and ‘g’, we get a new function ‘fg’ such as f(x). g(x) =fg (x)
4. Division: By dividing values of ‘f’ by ‘g’, we get a new function ‘f/g’ such as f(x)/g(x) = (f/g) (x)
5. Composition: By substituting the function ‘g’ in ‘f’, we get a new function ‘f o g’ such as (f o g) (x) = f(g(x))
Graphs of functions (function graphs)
The graph of function represents the all ordered pairs (x, f(x)) of the function. This means for each value of x there is a corresponding value of f(x) which is calculated by substituting the selected value of x in f(x).
For graphing the functions, following steps are followed: -
Select some random values of ‘x’.
Find out the corresponding value of f(x) by substituting the value of chosen value of ‘x’ in f(x).
Plot this point on the graph.
Repeat this process with at least six or seven points.
Join all the points to obtain the curve.
Resultant is the graph of the function.

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