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Magazine Problem 225
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
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
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\arctan (\ln (2 x-1)) $$
Problem 229
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccot}(\sqrt{2 x-1}) $$
Problem 230
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arcsec}(12 x) $$
Problem 231
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccsc}(x+5) $$
Problem 232
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arcsec}\left(\frac{x^{3}}{8}\right) $$
Problem 233
Find the domain of the given function. Write your answers in interval notation. $$ f(x)=\operatorname{arccsc}\left(e^{2 x}\right) $$
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 \(f(x)=\operatorname{arcsec}(x)\).
Problem 235
Show that \(\operatorname{arccsc}(x)=\arcsin \left(\frac{1}{x}\right)\) for \(|x| \geq 1\) as long as we use \(\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]\) as the range of \(f(x)=\operatorname{arccsc}(x)\)
