How do you find the domain of #f(x) = tan(3arccos(x))#?

1 Answer
Dec 15, 2017

Answer:

#"By combining domain of arccos(x) and tan(x), see explanation:"#
#[-1, 1] " \ {"-sqrt(3)/2", 0, "+sqrt(3)/2" }"#

Explanation:

#"arccos(x) is defined only for x "in" [-1, 1]."#
#"tan(x) is defined for all x values, except "pi/2 + k pi" , k integer."#
#"So we check : "#
#"3 arccos(x) = "pi/2 + k pi"."#
#=> arccos(x) = pi/6 + k pi/3"#
#=> x = cos(pi/6 + k pi/3)"#
#=> x = pm sqrt(3)/2, or 0#
#"For those 3 x-values, the function f(x) is not defined, so we have"#
#"as domain :"#
#[-1, 1] " \ {"-sqrt(3)/2", 0, "+sqrt(3)/2" }"#