What is the domain of f(x)=(2x+6)/(sqrt(-x^2-2x+48)) ?

The domain of f(x)=(2x+6)/(sqrt(-x^2-2x+48)) is -8<x<6

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domain of f(x)=(2x+6)/(sqrt(-x^2-2x+48))

domain

f (x) = \frac{2 x + 6}{- x ^{2} - 2 x + 48}

- 8 < x < 6

Interval Notation

(- 8, 6)

Solution steps

Find non-negative values for radicals:

- 8 \leq x \leq 6

Find undefined (singularity) points:

x = - 8, x = 6

Combine real regions and undefined points for final function domain

- 8 < x < 6

f (x) = \frac{3 x - 5}{4 - 3 x}

f (x) = \frac{x ( x ^{2} - 9 )}{x ^{2} - 4}

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

y = \frac{x}{x ^{2} - 9}

\frac{x ^{3} - 1}{\frac{1}{x}}

What is the domain of f(x)=(2x+6)/(sqrt(-x^2-2x+48)) ?
The domain of f(x)=(2x+6)/(sqrt(-x^2-2x+48)) is -8<x<6