Consider the following for the next items that follow:

Let $f(x)=\frac{a^{x-1}+b^{x-1}}{2}$ and g(x) = x - 1.

What is $\displaystyle \lim _{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}$ equal to?

Consider the following for the next items that follow:

Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$.

What is the domain of the function?

Consider the following for the next items that follow:

Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$.

What is the greatest value of the function?

Consider the following for the next items that follow:

Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function.

Let $ h(x)=\frac{f(g(x))}{g(f(x))}$.

What is $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?