Consider the functions \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\] Explain why $f$ and $g$ are not the same function.

\(Consider the functions \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\text{and}\\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]\)

Explain why f and g are not the same function

that it the way it was meant to be written