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

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

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

domain

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

x \leq - \frac{1}{2} or x > 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{2} or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{2} or x > 4

f (x) = ln (- 3 x + 6)

g (x) = 2 x^{2} - 4

\frac{5 - 3 x}{2}

y = x^{\frac{7}{3}} + x^{\frac{4}{3}} - 3 x^{\frac{1}{3}}

f (x) = \frac{8}{( \frac{x}{x - 9} )}

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