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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: captainoats on June 28, 2009, 05:26:53 pm

Title: Finding the domain from the INVERSE function?
Post by: captainoats on June 28, 2009, 05:26:53 pm: Hi there,

I have been given the following question:

The function f defined by f:A->R, where $f(x)=(x-3)^2+2$ , will have an inverse function if its domain A is:

A. R
B. R+ U {0}
C. {x:x $>=$ 2}
D. {x:x $<=$ 3}
E. {x:x $<=$ 1}

I have gone as far as working out the equation of the inverse: $y=\sqrt(x-2)+3$

And I know that the range of the inverse is equal to the domain of the original, but how do I work this out?

Thanks!
Title: Re: Finding the domain from the INVERSE function?
Post by: Flaming_Arrow on June 28, 2009, 05:33:07 pm: for an inverse function to exist, the function must be a one to one function. after u sketch the graph you can see the turning point is at x = 3 therefore the answer is D
Title: Re: Finding the domain from the INVERSE function?
Post by: captainoats on June 28, 2009, 05:34:55 pm: Quote from: Flaming_Arrow on June 28, 2009, 05:33:07 pm
for an inverse function to exist, the function must be a one to one function. after u sketch the graph you can see the turning point is at x = 3 therefore the answer is D

Sweet, thanks so much!
Title: Re: Finding the domain from the INVERSE function?
Post by: captainoats on June 28, 2009, 05:39:32 pm: I would give you karma, but, i havent reached 50 posts yet :-\