What is the domain of arccos(1/(x-3)) ?

The domain of arccos(1/(x-3)) is x = 4

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domain of arccos(1/(x-3))

domain

arccos (\frac{1}{x - 3})

x \leq 2 or x \geq 4

Interval Notation

(- \infty, 2] \cup [4, \infty)

Solution steps

Find known functions domain restrictions:

x \leq 2 or x \geq 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 2 or x \geq 4

\frac{1 - x}{2}

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

\frac{4 - 2 x ^{2}}{x ^{2} - 4 x + 3}

f (x) = 2 x^{2} + x + 10

\frac{9 x + 63}{9 x - 7}

What is the domain of arccos(1/(x-3)) ?
The domain of arccos(1/(x-3)) is x<= 2\lor x>= 4