What is the domain of f(x)=arcsin((|2x-4|-1)/(3x-5))arctan(sqrt(x^2-1)) ?

The domain of f(x)=arcsin((|2x-4|-1)/(3x-5))arctan(sqrt(x^2-1)) is x = 2

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domain of f(x)=arcsin((|2x-4|-1)/(3x-5))arctan(sqrt(x^2-1))

domain

f (x) = arcsin (\frac{∣ 2 x - 4 ∣ - 1}{3 x - 5}) arctan (x^{2} - 1)

x \leq - 1 or 1 \leq x \leq \frac{8}{5} or x \geq 2

Interval Notation

(- \infty, - 1] \cup [1, \frac{8}{5}] \cup [2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 1

Find known functions domain restrictions:

x \leq \frac{8}{5} or x \geq 2

Find undefined (singularity) points:

x = \frac{5}{3}

Combine real regions and undefined points for final function domain

x \leq - 1 or 1 \leq x \leq \frac{8}{5} or x \geq 2

\frac{2 x - 1}{x}

f (x) = \frac{2}{3} x + 1

f (x) = 3 x + 11

x^{2} - 2 x

What is the domain of f(x)=arcsin((|2x-4|-1)/(3x-5))arctan(sqrt(x^2-1)) ?
The domain of f(x)=arcsin((|2x-4|-1)/(3x-5))arctan(sqrt(x^2-1)) is x<=-1\lor 1<= x<= 8/5 \lor x>= 2