Question
Mon July 02, 2012 By:
 

Can you help me find out the range of the function f(x)=1/1-x square. x belongs to R.

Expert Reply
Tue July 03, 2012
Answer : given f(x) = 1/ (1 - x2 ) , x belongs to R
 
To find out the range of f(x),it is in the form of numerator / denomenator , we first check denominator should not be equal to zero.
i.e denominator not equal to 0
 
Therefore , in this question 1 - x 2 not equal to zero.
=> x = 1 or x = -1 not defined .
 
now we take if x value is greater than 1, then 
as x value increases, 1 - x2 is negative and quantity value increases,i.e greater than 1.
therefore at such instances 1 / value will decrease and will come in the range {0,1]
 
 
now we take if x value less than -1, then 
as x value decreases, 1 - x2, since x2 is always positive , then is negative and quantity value increases,i.e greater than 1.
therefore at such instances 1 / value will decrease and will come in the range {0,1]
 
now we take if x value is [0,1}, then 
as x value increases, 1 - x2 is positive, but less than 1.
therefore at such instances 1 / value will increase and will come in the range [1,2]
 
now we take if x value is {-1,0}, then 
as x value increases, 1 - x2 is positive, but less than 1.
therefore at such instances 1 / value will increase and will come in the range [1,2]
therefore , the range would come as {0,1] union [1,2] ={0,2] Answer

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