What is the domain of f(x)=sqrt((3x+5)/(2-x))+2 ?

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

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domain of f(x)=sqrt((3x+5)/(2-x))+2

domain

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

- \frac{5}{3} \leq x < 2

Interval Notation

[- \frac{5}{3}, 2)

Solution steps

Find non-negative values for radicals:

- \frac{5}{3} \leq x < 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- \frac{5}{3} \leq x < 2

5^{- \frac{x}{2}} + 5

- \frac{4 x}{x - 4} - \frac{2 x}{x + 2}

y = \frac{1}{x - 2} - 3

0 y = 5 x + 4

f (x) = (x)^{1} (x) = \frac{5 - 2 x}{4 x - 2}

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