# Mathematics: Relations and Functions-I: Logarithmic, Identify and Constant Functions

Get top class preparation for UGC right from your home: Get complete video lectures from top expert with unlimited validity: cover entire syllabus, expected topics, in full detail- anytime and anywhere & ask your doubts to top experts.

Download PDF of This Page (Size: 154K) ↧

## Logarithmic Functions

Now consider the function

We write it equivalently as , thus is the inverse function of

The base of the logarithm is not written if it is and so is usually written as.

## Identity Function

Let be the set of real numbers. Define the real valued function by for each. Such a function is called the identity function. Here the domain and range of are. The graph is a straight line. It passes through the origin.

## Constant Function

Define the function by where is a constant and each. Here domain of is and its range is . The graph is a line parallel to axis.

Example:

for each

## Signum Function

The function defined by following function is called a Signum function.

The domain of the signum function is R and the range is the set

The graph of the signum function is given as under: