Relationship between f(x) and f(1/x)

Uranium235

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)

willem2

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

Uranium235

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