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Suppose the domain of f is (-1,1). Define the function j by j(x)=f(1/x). What is the domain of j?

waffles  Oct 25, 2017
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  We have that the domain of f(x) is

 

- 1  < x <  1

 

Then the domain of  f ( 1/x)  is

 

-1  <  1/x  <  1    

 

-1 < 1/x       this will be true when  x < -1  and  x > 0

 

And

 

1/x < 1       this will be true when      x > 1

 

So.....we need to take the most restrictive interval(s)  in our solution

 

So the domain of  f (1/x)  is    ( - inf, -1)  U ( 1, inf )  = domain of j(x)

 

 

cool cool cool

CPhill  Oct 25, 2017
edited by CPhill  Oct 25, 2017

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