Question

What is a function?

Answer 1

To know what a function is we should first know what a set is because function is none other than the relation between two elements of a set. It is how one set is related to another. We know a set is a group of things that belong together or elements of a set possess the same nature.

Complete step-by-step solution:
The function is a relation between two sets or elements of a set where the set are never empty. In other ways a machine having both input and output and they are related somehow. The function of set $A$ and $B$ is defined as below:
$f:A\to B$
Where $a\in A$ has a unique element as $b\in B$ such that $\left( a,b \right)\in f$
If by chance we find another element in set $B$ which is related to element $a$ then it will no longer be a function. We can use other letters such as $g,h$ instead of $f$ if there is more function to be defined. Every function is considered as a relation but vice versa is not true.

Note: A function tells the relation between the elements of two sets or relation between the two sets. There are many types of function such as one-one function when each element of one set has a separate component of another set. Then there is a many-one function where more than two elements of the first set are mapped with one element of the second set. We have Linear and exponential functions also where exponential functions have extensive use in mathematics but linear function is the most used one.