Question

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of mc014-1.jpg?
u(x) mc014-2.jpg 0 and v(x) mc014-3.jpg 2
x mc014-4.jpg 0 and x cannot be any value for which u(x) mc014-5.jpg 2
x mc014-6.jpg 2 and x cannot be any value for which v(x) mc014-7.jpg 0
u(x) mc014-8.jpg 2 and v(x) mc014-9.jpg 0

Answer 1

I can't see the expression because the image files (mc014-1.jpg, etc.) didn't come through. Please either paste the function in text (for example "(u(x)-2)/v(x)" or "v(x)/(u(x)-2)") or reattach the image.

Meanwhile, here are the rules you can use to get the domain restrictions once I can see the expression:

- Always start with the domains of the inner functions: x cannot be 0 (because u is undefined there) and cannot be 2 (because v is undefined there) whenever u(x) or v(x) appears in the expression.
- Then exclude any x that makes a denominator 0. For example:
- If the expression is u(x)/v(x), exclude x where v(x) = 0 (and also x where u or v are undefined).
- If the expression is v(x)/(u(x)-2), exclude x where u(x) = 2 (and where u or v are undefined).
- If the expression is (u(x)-2)/v(x), exclude x where v(x) = 0 (and where u or v are undefined).
- Also exclude any x that makes other illegal operations (even root of a negative number, log of nonpositive number, etc.).

If you paste the exact function text, I'll give the precise domain restrictions.