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codpro880
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    codpro880
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f(x)  
« on: Jan 23rd, 2009, 12:59pm »		 Quote Quote Modify Modify
Let f(x) be a function such that f(x)+f(1/1-x)=x for all x
not equal to 0 or 1.
 
What is the value of f(2)?
 
 
 
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balakrishnan
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Re: f(x)  
« Reply #1 on: Jan 23rd, 2009, 1:13pm »		 Quote Quote Modify Modify

f(-1)+f(1/2)=-1
f(2)+f(-1)=2
f(1/2)+f(2)=1/2
Solving gives f(2)=7/4
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balakrishnan
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Re: f(x)  
« Reply #2 on: Jan 23rd, 2009, 1:47pm »		 Quote Quote Modify Modify
In general f(x)=(-x3 + x - 1)/(-2x2 + 2x)
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