Find the domain of the following functions. Make sure to use interval notation.
9.) Y=log(2x-12)
10.) Y=(x^2-4)/(2x+4)
11.) Y=(x^2-5x-6)/(x^2-3x-18)
12.) Y=2^(2-x)/x

Question

Find the domain of the following functions. Make sure to use interval notation.
9.) Y=log(2x-12) 
10.) Y=(x^2-4)/(2x+4)
11.) Y=(x^2-5x-6)/(x^2-3x-18)
12.) Y=2^(2-x)/x

anonymous · Answer

Please please help me!! I have no clue what they are even asking for!

anonymous · Answer

The domain of a function is the set where the function is well defined. when we deal with composition of functions we need to determinate the domain by evaluation order. For example for the function $$Y= \log (2x-12)$$ first we need to find the domain for $$2x-12$$ which is $$\mathbb{R} $$, next; the domain for $$\log(w)$$ is all $$w >0$$ hence if $$w=2x-12>0 \Longrightarrow x > 6$$ and that is the domain all $$x>6$$

anonymous · Answer

In the case when we have a quotient, the domain must exclude all points where the divisor (or denominator, I don't remember the exact name) is zero. For example for
$$Y=\frac{x^{2}-4}{2x+4}$$ there is one critical point in $$x=-2$$ but we can fix this with an algebraic manipulation
$$Y=\frac{x^{2}-4}{2x+4}=\frac{(x+2)(x-2)}{2 \cdot (x+2)}=\frac{x-2}{2}$$ and now the domain is all $$\mathbb{R}-\{-2\}$$