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

The domain of f(x)=sqrt(1/x+5) is x 0

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

domain

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

x \leq - \frac{1}{5} or x > 0

Interval Notation

(- \infty, - \frac{1}{5}] \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{5} or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - \frac{1}{5} or x > 0

f (x) = 5 x ∣ x ∣

(- 4, - 2), (6, - 10)

f (x) = \frac{6 x}{5 x - 8}

17 x (x - 1)^{3}

y = - \frac{3}{4} x + 2

What is the domain of f(x)=sqrt(1/x+5) ?
The domain of f(x)=sqrt(1/x+5) is x<=-1/5 \lor x>0