How do you find the domain of $f(x)=sqrt(4-x)$ ?

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Answer 1 · 2016-07-07T08:11:15

$Df(x) = x in R ; x > 4$

The domain is the set of $x$ -values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be $>= 0$ .

Therefore we need all of the $x$ -values that result in the value of $4 - x$ being $>= 0$ .

$4 -x >= 0$
$4 >= x$
$x <= 4$

So all $x$ -values $<= 4$ will work in the equation. Now we right this in terms of all real numbers:

The Domain of $x$ is all the real numbers expect when $x > 4$ (This produces a negative under the square root)

$Df(x) = x in R ; x > 4$

How do you find the domain of f(x)=sqrt(4-x)f(x)=sqrt(4-x)?