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Relationship between f(x) and f(1/x) 
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#1
Feb410, 08:31 PM

P: 13

Here's a problem that I am having difficulty doing:
1. The problem statement, all variables and given/known data The question states: if 2f(x)3f(1/x)=x^2, determine f(2) I am confused about the relationship between f(x) and f(1/x). My attempt right now consists of substituting y for f(x), 1/y for f(1/x) and 2 for the x in x^2 but i am quite sure that this is wrong since I do not get the answer that I was supposed to get (which is 7/4) 


#2
Feb410, 10:23 PM

P: 1,398

There is no relationship between f(x) and f(1/x) other then what you get from 2f(x)3f(1/x)=x^2. if y = f(x) then 1/y would be 1/f(x) and this is not equal to f(1/x)
You can try to substitute various values for x and see what you get if x = 1 this tells you that 2f(1)  3f(1) = 1 so f(1) = 1 if x=2 this tells you that 2f(2)  3f(1/2) = 4 now try to find another equation with f(2) in it 


#3
Feb510, 05:29 PM

P: 13

Thank you very much for the quick response. I was able to go from where you left off and get the correct answer.



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