Question

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

Answer 1

`"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" }"`