Question

Find (f + g)x, (f-g)x, (fg)x, and
(f/g)x and their domains.
f(x)=¡î(9-x©÷),g(x)=¡î(x©÷-4)

Answer 1

In western(ISO-8859-1) encoding, the post is:

Find (f + g)x, (f-g)x, (fg)x, and
(f/g)x and their domains.
f(x)=√(9-x²),g(x)=√(x²-4)

When posting mathematical symbols, you have more chances of being understood if you post directly in Western encoding.

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If you are working in the real domain (ℝ), you would want the results of the transformations to remain in ℝ.

For the +,- and * operations, the transformed domain would simply be D(f)∩D(g).

For the division, (f/g)(x), you will need to remove from D(f)∩D(g) points that do not exist in the transformed function. In the case of polynomials, this would generally be the values of x where g(x) becomes zero.

So if you get started with finding the domains of f(x) and g(x), you would have made a big step. All you need to do is to find the domains according to the rules above.

Post your answers for a check if you wish.