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

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

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

domain

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

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

Interval Notation

[- \frac{4}{3}, 2)

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

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

x^{2} - 6 x + 5

\frac{x + 2}{x - 3}

y = cos (5 x)

f (x) = \frac{1}{3} x^{3} - x^{2} - 8 x + 1

x^{2} + 7

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