What is the domain of f(x)=arccos(1/(2-x)) ?

The domain of f(x)=arccos(1/(2-x)) is x = 3

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domain of f(x)=arccos(1/(2-x))

domain

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

x \leq 1 or x \geq 3

Interval Notation

(- \infty, 1] \cup [3, \infty)

Solution steps

Find known functions domain restrictions:

x \leq 1 or x \geq 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq 1 or x \geq 3

f (x) = lo g_{2} (x - 1)

f (x) = x^{2} = - 2 y

f (x) = \frac{3}{lo g _{2} ( x ) - 4}

- 2 x + 3

f (x) = \frac{3}{2 x}

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