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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: geoff_821 on November 07, 2011, 09:46:27 pm

Title: f(g(x)) etc.
Post by: geoff_821 on November 07, 2011, 09:46:27 pm

What are the requirements for f(g(x)) to exist?

Title: Re: f(g(x)) etc.
Post by: taqi on November 07, 2011, 09:49:03 pm

range of g(x) must be equal to or part of the doman of f(x)

Title: Re: f(g(x)) etc.
Post by: thatisanote on November 07, 2011, 09:57:45 pm

which you write like ran g(x) <= (imagine a stretched c with an equals to) dom f(x)
where g(x) is the part inside the composite fn.

Title: Re: f(g(x)) etc.
Post by: david10d on November 07, 2011, 10:08:07 pm

what is the domain/range of f(g(x))

Title: Re: f(g(x)) etc.
Post by: Vincezor on November 07, 2011, 10:09:28 pm

Domain of f(g(x)) = dom g(x)

Range depends.. I think you have to work that one out using the domain...

Title: Re: f(g(x)) etc.
Post by: daliu on November 07, 2011, 10:14:32 pm

For f(g(x))

The range of g(x) must be restricted to the domain of f(x).

However, the overall domain of f(g(x)) is this restricted domain of g(x).

(Also, remember (f+g)(x)=f(x) + g(x) where the domain of (f+g) is dom f n dom g)

and (fg)(x)=f(x)g(x) where the domain of (fg) is dom f n dom g)

Title: Re: f(g(x)) etc.
Post by: abeybaby on November 07, 2011, 10:26:58 pm

range of f(g(x)) is the range of f over a domain of ran g.

Title: Re: f(g(x)) etc.
Post by: daliu on November 08, 2011, 11:15:28 am

It's amazing that you asked this question since it just came up on the Methods exam...lucky.