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

The domain of f(x)=sqrt(1+4/x) is x 0

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

domain

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

x \leq - 4 or x > 0

Interval Notation

(- \infty, - 4] \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 4 or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - 4 or x > 0

f (x) = \frac{6 x ^{2} + 5 x - 4}{2 x + 3}

f (x) = - 9

y = \frac{5 x}{3 - x x}

f (x) = 2 tan (\frac{π}{2} x)

What is the domain of f(x)=sqrt(1+4/x) ?
The domain of f(x)=sqrt(1+4/x) is x<=-4\lor x>0