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MATLAB, Wolfram Mathematica - software to compute mathematical functions.Lucy Joan Slater - British mathematician who studied about mathematical functions.Special functions can be elementary, non-elementary or inverses. Functions like f(x)=3x (three times x) are not called special functions. These include trigonometric functions such as sine, cosine and tangent. Special functions: Functions that have names.For example: if F(x) is the inverse of f(x)=y, then F(y)=x. Inverse functions - Functions that undo another function.Many integrals, for example, are non-elementary. Non-elementary functions - Most of them use operations that we don't learn in school (like + or -, or powers).Elementary functions - The functions that are usually studied in school: fractions, square roots, the sine, cosine and tangent functions and some other functions.The image of a function is a subset of its codomain and might not coincide with it. The set of all elements of the form f( x), where x ranges over the elements of the domain X, is called the image of f. X is called the domain of f, Y its codomain, and F its graph. A function is often denoted by italic letters such as f ). The set of all values that x can have is called the domain, and the set that contains every value that y can have is called the codomain. So a function is like a machine, that takes a value of x and returns an output y.