What is the domain of 1/(sqrt(-4x^2-20x-21)) ?

The domain of 1/(sqrt(-4x^2-20x-21)) is -7/2 <x<-3/2

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domain of 1/(sqrt(-4x^2-20x-21))

domain

\frac{1}{- 4 x ^{2} - 20 x - 21}

- \frac{7}{2} < x < - \frac{3}{2}

Interval Notation

(- \frac{7}{2}, - \frac{3}{2})

Solution steps

Find non-negative values for radicals:

- \frac{7}{2} \leq x \leq - \frac{3}{2}

Find undefined (singularity) points:

x = - \frac{7}{2}, x = - \frac{3}{2}

Combine real regions and undefined points for final function domain

- \frac{7}{2} < x < - \frac{3}{2}

What is the domain of 1/(sqrt(-4x^2-20x-21)) ?
The domain of 1/(sqrt(-4x^2-20x-21)) is -7/2 <x<-3/2