What is the domain of cos(1/x)sqrt((x-3)^2-4) ?

The domain of cos(1/x)sqrt((x-3)^2-4) is x = 5

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domain of cos(1/x)sqrt((x-3)^2-4)

domain

cos (\frac{1}{x}) (x - 3)^{2} - 4

x < 0 or 0 < x \leq 1 or x \geq 5

Interval Notation

(- \infty, 0) \cup (0, 1] \cup [5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 1 or x \geq 5

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq 1 or x \geq 5

What is the domain of cos(1/x)sqrt((x-3)^2-4) ?
The domain of cos(1/x)sqrt((x-3)^2-4) is x<0\lor 0<x<= 1\lor x>= 5