SOLUTION: 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

Question 1088256: 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.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

.....to find out what the domain and range are

{ element : or }
range:
{ : or }

domain:
{ element : }
range:
{ element : }
so, and are not same because they have different domain and range

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