Suppose that f is a function such that 3f(x)-5xf(1/x)=x-7 for all non-zero real numbers x. Find f(2010)
+6251 Suppose that f is a function such that 3f(x)-5xf(1/x)=x-7 for all non-zero real numbers x. Find f(2010)
\(3f(2010) - 5(2010)f\left(\dfrac 1 {2010}\right) = (2010)-7\)
\(3f(2010)-10050f\left(\dfrac 1 {2010}\right) = 2003\)
we can also write
\(3f\left(\dfrac 1 {2010}\right) - \dfrac {5}{2010}f(2010)=\dfrac 1{2010}-7=-\dfrac{14069}{2010}\)
\(let f(2010)=x, f\left(\dfrac 1 {2010}\right)=y\)
\(3x-10050y=2003\\ -\dfrac{5}{2010}x + 3y = -\dfrac{10469}{2010}\)
Solving this we get
\(x=2896\\\\ y = \dfrac{1337}{2010}\)
and thus
\(f(2010) = 2896\)
+6251 Suppose that f is a function such that 3f(x)-5xf(1/x)=x-7 for all non-zero real numbers x. Find f(2010)
\(3f(2010) - 5(2010)f\left(\dfrac 1 {2010}\right) = (2010)-7\)
\(3f(2010)-10050f\left(\dfrac 1 {2010}\right) = 2003\)
we can also write
\(3f\left(\dfrac 1 {2010}\right) - \dfrac {5}{2010}f(2010)=\dfrac 1{2010}-7=-\dfrac{14069}{2010}\)
\(let f(2010)=x, f\left(\dfrac 1 {2010}\right)=y\)
\(3x-10050y=2003\\ -\dfrac{5}{2010}x + 3y = -\dfrac{10469}{2010}\)
Solving this we get
\(x=2896\\\\ y = \dfrac{1337}{2010}\)
and thus
\(f(2010) = 2896\)
