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

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?