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

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

domain

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

x \leq - \frac{1}{2} or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{2} or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{2} or x > 3

lo g_{10} (2) lo g_{10} (10 x)

\frac{1}{2 x ( x - 8 ) ( 9 x + 5 )}

f (x) = \frac{1}{∣ x - 4 ∣ - 4}

f (x) = 16 - x^{2} - 4 - x

g (x) = \frac{1}{3 x}

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 \lor x>3