Home page for accesible maths Math 101 Chapter 2: Functions of a real variable 2.4 Functions, Domains and Codomains 2.6 Graphs and Continuity

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2.5 Real functions

In general, we can think of $f$ as a black box into which we feed a value of $x$ and out of which comes the value $f(x)$ . We think of $x$ as the input, and $f(x)$ as the output. The domain $A$ is the set of inputs, and the codomain is the set of all possible outputs; the range is set of actual outputs. The black box can be a calculator, a computer, or whatever.

Example

The tangent function is

g(x)=\tan x\qquad(x\neq\pm\pi/2,\pm 3\pi/2,\dots).

In calculus, we are mainly concerned with functions $f$ that depend upon a real variable $x$ , and such that $f(x)$ takes real values; we normally make the domain as large as we can, and choose the co-domain to be ${\mathbb{R}}.$ By tradition, we write $f(x)$ to indicate that the function $f$ is applied to the variable $x$ .