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Expert: - 5/4/2008


Question
if f(a)=max. (a,1/a) for all a>0 then find the value of     f(r)*f(1/r)
for all 0<r<1.


Answer
Questioner:   shweta
Category:  Calculus
Private:  No
 
Subject:  functions
Question:  if f(a)=max. (a,1/a) for all a>0 then find the value of     f(r)*f(1/r)
for all 0<r<1.
.......................
Hi, Shweta,

f(a) = max(a, 1/a) is the same as writing:

f(a) = a when a > 1, and 1/a when a < 1.

Now if  r < 1,

f(r) = 1/r, and  f(1/r) = r

So f(r) f(1/r) = (1/r) r = 1.

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