How do you find the domain and range of $f(x)=x$ ?

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Answer 1 · 2017-08-14T21:56:56

The domain of $f(x) = x$ is the whole of the real numbers $RR$ . The range is also the whole of $RR$ .

Given:

$f(x) = x$

The domain of $f(x)$ is the set of values for which $f(x)$ is defined. In the context of Algebra I that means a subset of the real numbers $RR$ . In the case of the given $f(x)$ , it is well defined for any $x in RR$ , so the domain is the whole of $RR$ , i.e. $(-oo, oo)$
The range of $f(x)$ is the set of values that it can take for some value of $x$ . Given any real number $y$ , let $x = y$ . Then $f(x) = x = y$ . So the range of $f(x)$ is the whole of $RR$ too.

The graph of $f(x) = x$ is a diagonal line like this:

# graph{x [-10, 10, -5, 5]}

For every $x$ coordinate there is a corresponding point on the line. That tells us that the domain of $f(x)$ is the whole of $RR$ .

For every $y$ coordinate there is a corresponding point on the line. That tells us that the range of $f(x)$ is the whole of $RR$ .

How do you find the domain and range of f(x)=xf(x)=x?