Functions- If 2f(x) - 3f(1/x) = x^2, determine f(2) Thanks

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Functions- If 2f(x) - 3f(1/x) = x^2, determine f(2) Thanks

Mathematics
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we can do this it requires a little work
in fact we can find a formula for \[f(x)\] if you like you pick
let's do the easy one you know \[2f(x)-3f(\frac{1}{x})=x^2\] so if you replace x by 2 you get \[2f(2)-3f(\frac{1}{2})=4\] and if you replace x by 1/2 you get \[2f(\frac{1}{2})-3f(2)=\frac{1}{4}\] which is the same as \[-3f(2)+2f(\frac{1}{2})=\frac{1}{4}\]

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Other answers:

so the basic idea is you are solving a system of equations like in algebra where you have \[2x-3y=4\] an d \[-3x+2y=\frac{1}{4}\]

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