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

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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.

Logarithmic Functions

Logarithmic Functions

Logarithmic Functions

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.

Identity Function

Identity Function

Identity Function

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

Example of Constant Function

Example of Constant Function

Example of Constant Function

Signum Function

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

Signum function

Signum Function

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:

The graph of the signum function

The Graph of the Signum Function

The graph of the signum function

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