For example, if f is a function that has the real numbers as domain and codomain, then a function mapping the value x to the value g(x) = 1 / f(x) is a function g from the reals to the reals, whose domain is the set of the reals x, such that f(x) ≠ 0 The range of a function is the set of the images of all elements in the domainThe = equals symbol is used to show that the values on either side of it are the same It is most commonly used to show the result of a calculation, for example 2 2 = 4, or in equations, such as 2 3 = 10 − 5 You may also come across other related symbols, although these are less common ≠ means not equal For example, 2 2 ≠ 5 2 Section 31 The Definition of the Derivative In the first section of the Limits chapter we saw that the computation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of an object at \(x = a\) all required us to compute the following limit \\mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right) f\left( a \right)}}{{x
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