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

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

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

domain

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

x \leq - \frac{1}{2} or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{2} or x > 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{2} or x > 5

(- 1, 1), (- 8, - 4)

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

f (x) = e^{(x)} (2 x^{2} + x - 8)

f (x) = - ∣ x ∣ + 3

f (x) = \frac{5 - x}{x}

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