Question

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

Answer 1

we can do this it requires a little work

Answer 2

in fact we can find a formula for
\[f(x)\] if you like
you pick

Answer 3

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
\[-3f(2)+2f(\frac{1}{2})=\frac{1}{4}\]

Answer 4

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