Functions and Inverse Functions
After the ideas of number and set, the next most important concept in mathematics is that of a function. Informally, a function is a rule which associated with each suitable input x, an output (or value) f(x). For example, we have the rule which associates with positive r, the value f(r) = πr2 which gives the area of a circle of radius r. Functions occur throughout mathematics and its applications. The typical scientific calculator has many of the most common functions built in (via the ‘function keys’). Such a calculator illustrates the need for using a ‘suitable input’—if we enter —1 and then press the √ key, we get an error message. The range of suitable inputs will, of course, vary with the choice ...
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