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

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

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

domain

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

- 4 < x \leq \frac{2}{3}

Interval Notation

(- 4, \frac{2}{3}]

Solution steps

Find non-negative values for radicals:

- 4 < x \leq \frac{2}{3}

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

- 4 < x \leq \frac{2}{3}

f (x) = 6 x^{2} + 26 x + 8

f (x) = - x^{2} - 4 x + 12

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

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

3 x - 4 y = 15

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