What is the domain of f(x)=(3x+4)/(sqrt(-x^2-2x+8)) ?

The domain of f(x)=(3x+4)/(sqrt(-x^2-2x+8)) is -4<x<2

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domain of f(x)=(3x+4)/(sqrt(-x^2-2x+8))

domain

f (x) = \frac{3 x + 4}{- x ^{2} - 2 x + 8}

- 4 < x < 2

Interval Notation

(- 4, 2)

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 2

Find undefined (singularity) points:

x = - 4, x = 2

Combine real regions and undefined points for final function domain

- 4 < x < 2

2 x - 3

f (x) = \frac{x}{x - 8}

f (x) = lo g_{10} (2 x - 2)

f (x) = \frac{3}{∣ x - 2 ∣}

\frac{x + 8}{4 x + 12}

What is the domain of f(x)=(3x+4)/(sqrt(-x^2-2x+8)) ?
The domain of f(x)=(3x+4)/(sqrt(-x^2-2x+8)) is -4<x<2