What is the domain of f(x)=sqrt(x^2+x)-x ?

The domain of f(x)=sqrt(x^2+x)-x is x = 0

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domain of f(x)=sqrt(x^2+x)-x

domain

f (x) = x^{2} + x - x

x \leq - 1 or x \geq 0

Interval Notation

(- \infty, - 1] \cup [0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 0

The function domain

x \leq - 1 or x \geq 0

y = 2 (x - 2)

y = - 18

f (x) = \frac{1}{4 x ^{2} + 8}

\frac{1}{2}

y = \frac{2}{3} x + 7 (6.4)

What is the domain of f(x)=sqrt(x^2+x)-x ?
The domain of f(x)=sqrt(x^2+x)-x is x<=-1\lor x>= 0