What is the domain of f(x)=sqrt((2x-1)/(x+3)) ?

The domain of f(x)=sqrt((2x-1)/(x+3)) is x = 1/2

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domain of f(x)=sqrt((2x-1)/(x+3))

domain

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

x < - 3 or x \geq \frac{1}{2}

Interval Notation

(- \infty, - 3) \cup [\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x < - 3 or x \geq \frac{1}{2}

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or x \geq \frac{1}{2}

f (x) = \frac{x + 6}{2 x - 4}

f (x) = x^{3} - 3 x + 27

3 sin (x)

f (x) = 1 - x

f (x) = \frac{x + 1}{x ^{2} - 3 x - 4}

What is the domain of f(x)=sqrt((2x-1)/(x+3)) ?
The domain of f(x)=sqrt((2x-1)/(x+3)) is x<-3\lor x>= 1/2