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Magazine Problem 223
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\arccos \left(\frac{3 x-1}{2}\right) $$
Problem 224
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\arcsin \left(2 x^{2}\right) $$
Problem 226
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\arccos \left(\frac{1}{x^{2}-4}\right) $$
Problem 227
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccot}\left(\frac{2 x}{x^{2}-9}\right) $$
Problem 228
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\arctan (\ln (2 x-1)) $$
Problem 229
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccot}(\sqrt{2 x-1}) $$
Problem 230
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arcsec}(12 x) $$
Problem 231
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccsc}(x+5) $$
Problem 232
In Exercises 222 - 233 , find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arcsec}\left(\frac{x^{3}}{8}\right) $$
Problem 234
Show that \(\operatorname{arcsec}(x)=\arccos \left(\frac{1}{x}\right)\) for \(|x| \geq 1\) as long as we use \(\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]\) as the range of \(f(x)=\operatorname{arcsec}(x)\)
