Section: Analysis




The definition of a Function

Domain and Range of a function

Inverse Functions


Calculating the inverse function


The origin of the concept of functions has always been closely linked to the study of the phenomena of change. The oldest written references can be found amongst the writings of Babylonian astronomers. In the Middle Ages the study of functions appeared to be linked to the concept of movement. Nicole Oresme (1323-1392), a scholar interested in this concept, gave graphical representations showing change in velocity with respect to time.

Three centuries later, Galileo studied movement from a quantitative point of view, justified his discoveries experimentally and established laws between different magnitudes. 

After Galileo, the concept of the function evolved until, in the XIXth century, in 1837, Dirichlet defined the function as a relation between variables, which is the definition we still use today.

Functions are a basic tool which are used in physics, biology, social sciences and so on.

  • Recognise a function graphically
  • Find the domain and range of a function both graphically and analytically
  • Use the graph of a function to see if it has an inverse.

  • Find the inverse of a few simple functions using analytical methods.
  • Use a graph to find the table of values of an inverse function for more complex functions.

  Salvador Calvo-Fernández Pérez
Spanish Ministry of Education and Education. Year 2001

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