Question
Fri July 06, 2012 By: Riya Kardon

Find the range of of the following:

Expert Reply
Fri July 06, 2012
Answer (i) : Given :  f(x)= 1/(sqare root ( x - 5 ) )
                    To find : range of f(x)
          
           let y = f(x)
           => y = 1/ (sqare root(x-5) )
               squaring and inversing it, we get
              => 1/ y2 = x - 5
               => x = ( 1/ y2 ) + 5
 let x = g(y) = ( 1/ y2 ) + 5
 => range of f(x) = domain of g(y)  
therefore , the domain of g(y) is R - {0 } which is range of f(x)
 
 
(ii) : Given :  f(x)= 1/(sqare root (16 - x 2) )
                    To find : range of f(x)
          
           let y = f(x)
           => y = 1/ (sqare root(16 - x2) )
               squaring and inversing it, we get
              => 1/ y2 = 16 -x2
               => x2 = 16 - ( 1/ y2
                => x = square root ( 16 - ( 1/ y2 ) )
 let x = g(y) = square root ( 16 - ( 1/ y2 ) )

=> range of f(x) = domain of g(y)  
 
therefore , the domain of g(y) is R - {0 } which is range of f(x)

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