What is the domain of f(x)=sqrt((2x-1)/(3x+4)) ?

The domain of f(x)=sqrt((2x-1)/(3x+4)) is x = 1/2

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domain of f(x)=sqrt((2x-1)/(3x+4))

domain

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

x < - \frac{4}{3} or x \geq \frac{1}{2}

Interval Notation

(- \infty, - \frac{4}{3}) \cup [\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x < - \frac{4}{3} or x \geq \frac{1}{2}

Find undefined (singularity) points:

x = - \frac{4}{3}

Combine real regions and undefined points for final function domain

x < - \frac{4}{3} or x \geq \frac{1}{2}

What is the domain of f(x)=sqrt((2x-1)/(3x+4)) ?
The domain of f(x)=sqrt((2x-1)/(3x+4)) is x<-4/3 \lor x>= 1/2