What is the domain of (sqrt(2x+7))/(x-|x|) ?

The domain of (sqrt(2x+7))/(x-|x|) is -7/2 <= x<0

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domain of (sqrt(2x+7))/(x-|x|)

domain

\frac{2 x + 7}{x - ∣ x ∣}

- \frac{7}{2} \leq x < 0

Interval Notation

[- \frac{7}{2}, 0)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{7}{2}

Find undefined (singularity) points:

x \geq 0

Combine real regions and undefined points for final function domain

- \frac{7}{2} \leq x < 0

(x + 9)^{2} - 3

x^{2} - 81

f (x) = 2 x - x^{2} + 8

y = 8 - 4 x

f (x) = x + 17

What is the domain of (sqrt(2x+7))/(x-|x|) ?
The domain of (sqrt(2x+7))/(x-|x|) is -7/2 <= x<0