Author Topic: composite implied domains (Read 1392 times) Tweet Share

pHysiX · « **on:** April 20, 2009, 07:20:33 pm »

What is the implied domain of:
$ {\sin ^{ - 1}}\left[ {\cos \left( { - 2x} \right)}] $

TrueTears · « **Reply #1 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 $dom f o g = dom g = R$

pHysiX · « **Reply #2 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:
$\begin{array}{l} \left[ {\frac{{ - \pi }}{2},0} \right] \\ \left[ {0,\frac{\pi }{2}} \right] \\ \left[ { - \pi ,\pi } \right] \\ \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right] \\ \left[ { - 2\pi ,2\pi } \right] \\ \end{array}$

TrueTears · « **Reply #3 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.

pHysiX · « **Reply #4 on:** April 20, 2009, 07:41:14 pm »

nope
that's the exact question =]

TrueTears · « **Reply #5 on:** April 20, 2009, 07:42:09 pm »

Then the choices they gave are wrong

pHysiX · « **Reply #6 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

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