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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=sqrt%28%28x%2B1%29%2F%28x-1%29%29.....to find out what the domain and range are

{ x element R : x%3C=-1 or x%3E1 }
range:
{ f%28x%29+element+%7B%7B%7BR : 0%3C=f%28x%29%3C1 or f%28x%29%3E1 }


g%28x%29=sqrt%28%28x%2B1%29%29%2Fsqrt%28%28x-1%29%29
domain:
{ x element R : x%3E1 }
range:
{ g%28x%29 element R : g%28x%29%3E1 }
so, f%28x%29 and g%28x%29 are not same because they have different domain and range