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EEMILY33 · Mar 12, 2009, 08:22 AM

Cosider the functions f and g defined as follows.
f(x) = x-3/x-2 for all x E R, does not equal 2.
g(x) = 3-x for all x E R.
Find all possible functions that are generated by composing the functions f and g. After finding all functions, prove that you have them all and identify the domain of each. You will want to look at (f of g), g of f, f of f, g of g, f of(g of f) and so on.

Curlyben · Mar 12, 2009, 08:25 AM

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galactus · Mar 13, 2009, 03:45 PM

Composing functions just means you sub one function into the other.

For instance, f of g. Plug g in for x in f.

$f(g(x))=\frac{(3-x)-3}{(3-x)-2}=\frac{-x}{1-x}=\frac{x}{x-1}$

$f(f(x))=\frac{\frac{x-3}{x-2}-3}{\frac{x-3}{x-2}-2}=\frac{2x-3}{x-1}$

Now, you try the others and let's see what you get.

The domain of the first and last ones is everything except 1, because x=1 will result in division by 0.

Askmeexperrt21 · Mar 13, 2009, 03:47 PM

Is this even logical?

galactus · Mar 13, 2009, 03:56 PM

What do you mean, is it logical? They are just composite functions.