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

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

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

domain

f (x) = \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}

ln (x + 5)

f (x) = 15 - 2 x + 2 x + 5

f (x) = ln (1 + x^{2})

f (x) = \frac{( 2 x ^{2} - 6 x + 4 )}{- 3 x - 5}

1.5 - 3 x

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