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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: run-bandit on February 21, 2010, 09:46:43 pm

Title: amirite?
Post by: run-bandit on February 21, 2010, 09:46:43 pm

Is this the 'answer' before you have put it into a CAS calculator for this question (since working out is not provided in the book)

Question:

f(x) = 2 g(x-2) + 1 and g(x) = sqrt(x), find f(x) in terms of x only using matrices and a CAS calculator

Answer:

[ 2 0 ] ( [   x  ] + [ -1 ] )
[ 0 1 ] ( [ g(x) ]   [ -2 ] )

If it is not - why so?

Title: Re: amirite?
Post by: the.watchman on February 21, 2010, 10:08:31 pm

I think you want the following:

[ x' ] = [ 1 0 ] [ x ] + [ 2 ]
[ y' ]    [ 0 2 ] [ \sqrt{x} ]    [ 1 ]

NOTE: it is a dilation by factor 2 from x-axis, not y, and the translations are 2 right (+2 for x in matrix form) and 1 up (+1 for y in matrix form)

So (1)

, (2)

sub (2) into (1):



I hope this is considered to be 'all matrices' :P

Good luck!