ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: pHysiX on April 20, 2009, 07:20:33 pm

Title: composite implied domains
Post by: pHysiX on April 20, 2009, 07:20:33 pm: What is the implied domain of:
$ {\sin ^{ - 1}}\left[ {\cos \left( { - 2x} \right)}] $
Title: Re: composite implied domains
Post by: TrueTears on April 20, 2009, 07:32:31 pm: Let $sin^{-1}(x) = f(x)$

and $cos(-2x) = g(x)$

for $f o g$ to exist $ran g \subset dom f$

$ran g = [-1,1]$

$dom f = [-1,1]$

so $ran g \subset dom f$ , no restrictions required

so $dom f o g = dom g = R$
Title: Re: composite implied domains
Post by: pHysiX on April 20, 2009, 07:37:50 pm: haha *hi5* that's wat i got as well...

too bad the multiple choice options don't have that >.<

they have:
$\begin{array}{l} \left[ {\frac{{ - \pi }}{2},0} \right] \\ \left[ {0,\frac{\pi }{2}} \right] \\ \left[ { - \pi ,\pi } \right] \\ \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right] \\ \left[ { - 2\pi ,2\pi } \right] \\ \end{array}$
Title: Re: composite implied domains
Post by: TrueTears on April 20, 2009, 07:39:30 pm: Are you sure they didn't give an restriction on the $cos$ function?

Because they tend to restrict the domain for these questions.
Title: Re: composite implied domains
Post by: pHysiX on April 20, 2009, 07:41:14 pm: nope
that's the exact question =]
Title: Re: composite implied domains
Post by: TrueTears on April 20, 2009, 07:42:09 pm: Then the choices they gave are wrong :)
Title: Re: composite implied domains
Post by: pHysiX on April 20, 2009, 07:43:07 pm: wooties! *hi5* that's another thing wrong to add to the list of wrong things =] thanks TT