Are There Any Exceptions to the Rule for Domain Exclusions?

[Qube]

Homework Statement

http://i.minus.com/jbiWoIFy45kCgV.png

Homework Equations

The denominator of a function cannot equal 0. Both the numerator and denominator also cannot = 0 simultaneously.

The Attempt at a Solution

For the first problem, the denominator and the numerator are 0 when x =0. Hence, I excluded it from the domain. Similarly, for the second problem, the denominator is 0 when x = -8. It is also excluded from the domain. Am I missing something?

 

[Dick]

Homework Statement

http://i.minus.com/jbiWoIFy45kCgV.png

Homework Equations

The denominator of a function cannot equal 0. Both the numerator and denominator also cannot = 0 simultaneously.

The Attempt at a Solution

For the first problem, the denominator and the numerator are 0 when x =0. Hence, I excluded it from the domain. Similarly, for the second problem, the denominator is 0 when x = -8. It is also excluded from the domain. Am I missing something?

Yes, a little. You can't just look at the final formula. Take the first one. g(x) is undefined at x=(-1). If g(-1) is undefined then f(g(-1)) isn't defined either.