The functions $f$ and $g$ are defined as follows: \[f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\]Explain why the functions $f$ and $g$ are not the same function.
+128474 \(f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}\)
Note that f(x) will be defined whenever x ≤ - 1 and x > 1
But note that g(x) is only defined whenever x > 1......
See the graph here to get a feel for this :
https://www.desmos.com/calculator/lhfhhtc98o
