Home page for accesible maths Math 101 Chapter 2: Functions of a real variable 2.2 Functions of a real variable chapter contents 2.4 Functions, Domains and Codomains

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2.3 Functions

Here $x$ is a real variable; that is, a point that varies along the real line. Everyone is familiar with the notion of a formula, but when does a formula determine a valid real function?

2.3.1 Example

$f(x)=2x^{2}-1$ . This makes sense for all real $x$ , so we can specify

f:{\mathbb{R}}\rightarrow{\mathbb{R}}\quad{\hbox{ given by}}\quad f(x)=2x^{2}-1.

2.3.2 Example

$g(x)=\tan x.$ Here $x$ is an angle in radians, and we take $-\pi/2<x<\pi/2$

g:\qquad\qquad\rightarrow{\mathbb{R}}\quad{\hbox{ given by}}\quad g(x)=\tan x.