What do we mean when we say that 3.14 is an approximation of π ? This means that on the real line these two numbers are ‘close’ to each other. The numbers −7.1 and −7 are closer to each other than the pair 10 and −1000. The modulus function is useful to measure the distance between two numbers. |x| is just the distance between origin and the point x. We formally define the modulus function || : ℝ → ℝ+ as follows.
The distance between two points x and y is nothing but |x − y|. The statement |x| ≤ a is equivalent to the statement −a ≤ x ≤ x.
Show that the function f : ℝ → ℝ defined as f(x