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

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

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}

\frac{8 x}{x ^{2} - 64}

\frac{2 x - 1}{9 x + 5}

f (x) = \frac{1}{- x ^{2} + 9 x + 10}

f (x) = (x + 2)^{3} - 3

f (x) = (x + 2)^{3} - 2

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