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1. C3 functions range and domain
$f(x) = x - 3, g(x) = +\sqrt{x}$

Find gf(x) and a suitable domain and the corresponding range.

so $gf(x) = \sqrt{x-3}$, f(x) is first and the domain for f(x) is x belongs to R(all the real numbers), so the domain for g(x) will be x belongs to R, so this function doesn't work?

the answer is the domain is x>=3 and the range is x>=0, which I understand how they got but watching videos online and they separate each function, i.e do f(x) first, and find the domain and range for that, then the range becomes the domain for g(x), now I don't understand which way is correct
2. Re: C3 functions range and domain
Personally I think it's much easier to find gf(x) first, then work out the domain and/or range. I've never done it by finding domain and range separately but I'm sure it's not too difficult

fg(x) = sqrt(x-3)

Therefore x cannot be less than 3, because you cannot obtain a REAL number from square rooting a negative number.

so x > (or equal to) 3 (domain)

gf(x), on the other hand, can take any value which is positive, just try values in your head like x = 3, x = 4, etc. REMEMBER, the x-values MUST be within the domain.

so range is gf(x) > (or equal to) 0
Last edited by Anythingoo1; 08-08-2012 at 01:29.
3. Re: C3 functions range and domain
(Original post by syNK)
$f(x) = x - 3, g(x) = +\sqrt{x}$

Find gf(x) and a suitable domain and the corresponding range.

so $gf(x) = \sqrt{x-3}$, f(x) is first and the domain for f(x) is R, so the domain for g(x) will be R, so this function doesn't work?

the answer is the domain is x>=3 and the range is x>=0, which I understand how they got but watching videos online and they separate each function, i.e do f(x) first, and find the domain and range for that, then the range becomes the domain for g(x), now I don't understand which way is correct
This is your mistake. You know the domain and range of f(x) is R, and the domain and range of g(x) is x positive or zero. So you should be looking for what domain of f(x) will give you the appropriate range that suits the domain of g(x).

Basically, whatever is nested in g(x) must be positive or zero, so look for what values of x you will have f(x) positive or zero (since f(x) is nested in g(x)).