Crazy Functions

Alternatively, the solution steps can be done using a symbolic algebra system, in this case sympy. You still must know how to solve the problem.

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>>> from sympy import *
>>> var('x')
x
>>> f=Function('f')
>>> ex=Eq(f(1/x)-3*f(x),x)
>>> ex.subs(x,2)
f(1/2) - 3*f(2) == 2
>>> ex.subs(x,Rational(1,2))
-3*f(1/2) + f(2) == 1/2
>>> solve([f(Rational(1,2))-3*f(2)-2,-3*f(Rational(1,2))+f(2)-Rational(1,2)])
[{f(2): -13/16, f(1/2): -7/16}]
>>> N(Rational(-13,16))
-0.812500000000000

Create a system of equations with two variables. In this case, 2 and $\frac{1}{2}$ would be smart to use for x as there will only be two variables, $f\left( 2 \right)$ and $f\left( \frac { 1 }{ 2 } \right)$ . $1.\quad f\left( \frac { 1 }{ 2 } \right) -3f\left( 2 \right) =2\\ 2.\quad f\left( 2 \right) -3f\left( \frac { 1 }{ 2 } \right) =\frac { 1 }{ 2 }$ Now, substitute and solve. Isolating $f\left(2\right)$ in equation 2: $f\left( 2 \right) =\frac { 1 }{ 2 } +3f\left( \frac { 1 }{ 2 } \right)$ Substituting into equation 1: $f\left( \frac { 1 }{ 2 } \right) -3\left( \frac { 1 }{ 2 } +3f\left( \frac { 1 }{ 2 } \right) \right) =2\\ f\left( \frac { 1 }{ 2 } \right) -\frac { 3 }{ 2 } -9f\left( \frac { 1 }{ 2 } \right) =2\\ -8f\left( \frac { 1 }{ 2 } \right) =\frac { 7 }{ 2 } \\ f\left( \frac { 1 }{ 2 } \right) =-\frac { 7 }{ 16 }$ Plugging back into equation 1: $-\frac { 7 }{ 16 } -3f\left( 2 \right) =2\\ -3f\left( 2 \right) =\frac { 39 }{ 16 } \\ f\left( 2 \right) =-\frac { 13 }{ 16 } \\ f\left( 2 \right) =\boxed { -0.8125 }$

plug in 1/x and then solve f(x) you get: -(3x/8+1/8x) plug in 2 and you'r done