This is usually read "f of x." We also call f(x) the value of f at x.
In terms of the pictorial representation given earlier, we may now sketch a diagram as in Figure 1.18.
For each book x in X there corresponds a positive integer y, namely the number of pages in the book.
In the second example, if we let X denote the set of all human beings and Y the set of all possible dates, then to each person x in X there corresponds a birth date y. Our examples indicate that to each x in X there corresponds one and only one y in Y; that is, y is unique for a given x.
Beginning students are sometimes confused by the symbols f and f(x). Two functions f and g from X to Y are said to be equal, written for every x in X.
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Example 1 Let f be the function with domain R such that f(x) = x, where a is a real number.Moreover, every nonnegative real number c is an image underf, since .Hence the range of f is the set of all nonnegative real numbers.The element y is called the image of x under f and is denoted by f(x). The range of the function consists of all images of elements of X.Earlier, we introduced the notation f(x) for the element of Y which corresponds to x.The letter r, which represents an arbitrary number from the domain off, is often called an independent variable.The letter A, which represents a number from the range off, is called a dependent variable, since its value depends on the number assigned tor.Since the square of any real number is nonnegative.T is contained in the set of all nonnegative real numbers.While the 5 steps of Algebra problem solving are listed below, this article will focus on the first step, Identify the problem.Back away from the calculator; use your brain first.