## Adam555 Group Title Functions- If 2f(x) - 3f(1/x) = x^2, determine f(2) Thanks 2 years ago 2 years ago

1. satellite73 Group Title

we can do this it requires a little work

2. satellite73 Group Title

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

3. satellite73 Group Title

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

4. satellite73 Group Title

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