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

Guest Mar 14, 2018

#1**+2 **

\( f(x) = \sqrt{\dfrac{x+1}{x-1}}\qquad\qquad\)

\(\qquad\qquad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}.\)

If these functions are the same, they have the same domain.....

Notice that the domain of the first function is (-inf, -1) U (1, inf )

But the domain of the second function is only (1, inf)......any negative in the denominator makes this function undefined for the set of real numbers.....

So....these functions are not the same

CPhill Mar 15, 2018