What is the domain of the function $1/(x^2+x+1)+x$ ?

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Answer 1 · 2017-04-02T10:21:27

$RR$

Notice that:

$x^2+x+1 = (x+1/2)^2+3/4$

So:

$x^2+x+1 >= 3/4 > 0$ for all real values of $x$

Hence, for any real value of $x$ , the given expression:

$1/(x^2+x+1)+x$

is well defined.

So the domain is the whole of the real numbers $RR$ .

What is the domain of the function 1/(x^2+x+1)+x1/(x^2+x+1)+x ?