What is the domain of f(x)=sqrt((4x-5)/(1+2x)) ?

The domain of f(x)=sqrt((4x-5)/(1+2x)) is x = 5/4

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domain of f(x)=sqrt((4x-5)/(1+2x))

domain

x < - \frac{1}{2} or x \geq \frac{5}{4}

Interval Notation

(- \infty, - \frac{1}{2}) \cup [\frac{5}{4}, \infty)

Solution steps

Find non-negative values for radicals:

x < - \frac{1}{2} or x \geq \frac{5}{4}

Find undefined (singularity) points:

x = - \frac{1}{2}

Combine real regions and undefined points for final function domain

x < - \frac{1}{2} or x \geq \frac{5}{4}

What is the domain of f(x)=sqrt((4x-5)/(1+2x)) ?
The domain of f(x)=sqrt((4x-5)/(1+2x)) is x<-1/2 \lor x>= 5/4