What is the domain of f(x)= 1/(sqrt(10-3x-x^2)) ?

The domain of f(x)= 1/(sqrt(10-3x-x^2)) is -5<x<2

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domain of f(x)= 1/(sqrt(10-3x-x^2))

domain

f (x) = \frac{1}{10 - 3 x - x ^{2}}

- 5 < x < 2

Interval Notation

(- 5, 2)

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 2

Find undefined (singularity) points:

x = - 5, x = 2

Combine real regions and undefined points for final function domain

- 5 < x < 2

f (x) = sin (x^{l n (x)})

lo g_{3} (x^{2} - 9)

f (x) = \frac{3 x}{x - 6}

f (x) = 3 x^{2} - \frac{1}{2} x + 5

f (x) = \frac{5 x}{7 x - 1}

What is the domain of f(x)= 1/(sqrt(10-3x-x^2)) ?
The domain of f(x)= 1/(sqrt(10-3x-x^2)) is -5<x<2