# Functions

## Inverse functions

Let $$X$$ and $$Y$$ be two sets, and $$f$$ be a one-to-one function defined by $$f:{X} \rightarrow Y$$ with domain $$X$$ and range $$Y$$. Then, $$f^{-1}:{Y} \rightarrow X$$ is called the inverse function. Here, $$f^{-1}\left ( x\right )$$ does not mean $$\frac{1}{f\left (x \right )}$$.

## Functions

A function can be thought of as two sets. Let $$X$$ and $$Y$$ be two sets and $$f$$ be the function from the set $$X$$ to $$Y then the function$$f$$is defined as$$ f:X\rightarrow Y$$. Here, the set$$X$$is called the domain or the set of inputs and set$$Y$$is the range or the set of outputs. The function$$f$$associated with each element is$$x$$in$$X$$with one and only element$$y$$in$$Y.