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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Thymaster on February 13, 2013, 08:43:17 pm

Title: Unique solutions and composite fns
Post by: Thymaster on February 13, 2013, 08:43:17 pm: wth is a unique solution and also how do u determine the domain of f(g(x))
Title: Re: Unique solutions and composite fns
Post by: Daenerys Targaryen on February 13, 2013, 08:45:41 pm: Well:
Unique solution: has a solution, essentially point of intersection, or a solution that exists
The domain of $f(g(x))$ is given by the domain of $g(x)$ given that the domain of g(x) has undergone the restrictions necessary.
Title: Re: Unique solutions and composite fns
Post by: polar on February 13, 2013, 09:02:15 pm: $x \mapsto g(x) \mapsto f(g(x))$ (you put x values into g(x) and then put these g(x) values into f(x))

what's the domain of the function at the end? it's the range of g(x). (which is why you need to have $\mathrm{ran}g \subseteq \mathrm{dom}f$ ). now lets look at the middle, what gave you the range of g(x) in the first place? the x values at the start. hence, the domain of f(g(x)) is the domain of g as long as the range of g is a subset of equal to the domain of f. (otherwise you'd need to restrict it first)
Title: Re: Unique solutions and composite fns
Post by: Harley2262 on February 15, 2013, 11:51:13 pm: I've been having the same problem too lately. Can someone please explain what the question exactly is asking for in regards to unique solution, no solution or infinitely many solutions? I know WHAT they mean but not how to prove it.
Title: Re: Unique solutions and composite fns
Post by: b^3 on February 16, 2013, 12:51:26 am: Quote from: Harley2262 on February 15, 2013, 11:51:13 pm
I've been having the same problem too lately. Can someone please explain what the question exactly is asking for in regards to unique solution, no solution or infinitely many solutions? I know WHAT they mean but not how to prove it.
You mean regarding straight lines right?
Theres a post that I typed up a little while ago that went through it (as long as I've read what you mean right).

Re: Methods [3/4] Question Thread!

Goes through both the rearranging and matrix methods.