What is the domain of f(x)=(2x+6)/(sqrt(-x^2-5x+24)) ?

The domain of f(x)=(2x+6)/(sqrt(-x^2-5x+24)) is -8<x<3

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domain of f(x)=(2x+6)/(sqrt(-x^2-5x+24))

domain

f (x) = \frac{2 x + 6}{- x ^{2} - 5 x + 24}

- 8 < x < 3

Interval Notation

(- 8, 3)

Solution steps

Find non-negative values for radicals:

- 8 \leq x \leq 3

Find undefined (singularity) points:

x = - 8, x = 3

Combine real regions and undefined points for final function domain

- 8 < x < 3

y = \frac{1}{2} x - 1

9 x - 8

y = 5 x 2, (1, 1)

f (x) = - 6 x + 2

y = - 3 tan (\frac{1}{2} x)

What is the domain of f(x)=(2x+6)/(sqrt(-x^2-5x+24)) ?
The domain of f(x)=(2x+6)/(sqrt(-x^2-5x+24)) is -8<x<3