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4 Calculus of functions of one variable 4.1 Functions, range, domain A  function  is a rule that assigns a unique value  f (x) to each value  x in a given  domain. The set of values taken by  f (x) when  x  takes all possible values in the domain is the  range  of  f . 4.1.1 Example  f (x) = x 2 for − 1 < x 1 x 1 1 -1 O domain of f of f range y=f(x) y 1 4.2 Some important functions 4.2.1 Exponential function f (x) = exp x  may be dened by  df (x) dx  = f (x) and  f (0) = 1. O 1 x exp(x) Exponential function is denoted by f (x) = e x or exp x for all real  x. 2

Calculus and Functions

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