+0  
 
0
52
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar+85821 
+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

 

 

cool cool cool

CPhill  Mar 15, 2018

35 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details