What is the domain of f(x)=(3x+8)/(sqrt(-x^2-6x+16)) ?

The domain of f(x)=(3x+8)/(sqrt(-x^2-6x+16)) is -8<x<2

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domain of f(x)=(3x+8)/(sqrt(-x^2-6x+16))

domain

f (x) = \frac{3 x + 8}{- x ^{2} - 6 x + 16}

- 8 < x < 2

Interval Notation

(- 8, 2)

Solution steps

Find non-negative values for radicals:

- 8 \leq x \leq 2

Find undefined (singularity) points:

x = - 8, x = 2

Combine real regions and undefined points for final function domain

- 8 < x < 2

f (x) = \frac{x - 1}{x + 1}

f (x) = \frac{13}{3 x + 13}

f (x) = x^{2} + 8 x - 20

f (x) = \frac{1}{ln ( x + 1 )}

- (\frac{1}{4})^{x} - 2

What is the domain of f(x)=(3x+8)/(sqrt(-x^2-6x+16)) ?
The domain of f(x)=(3x+8)/(sqrt(-x^2-6x+16)) is -8<x<2