As we’re hoping to evaluate f(4) we might try letting x = 4 initially:

2*f(-3) – f(4) = 540

But now we need to know the value of f(-3), so:

2*f(1/2) - f(-3)= -405

We plough on:

2*f(6/5) - f(1/2) = 135/2

2*f(5/3) - f(6/5) = 162

2*f(9/4) - f(5/3) = 225

And just as we start to lose hope:

2*f(4) - f(9/4) = 1215/4

So now we have 6 equations in 6 unknowns, let’s multiply the second equation by 2, the next by 4, the next by 8 etc:

2*f(-3) - f(4) = 540

4*f(1/2) - 2*f(-3) = -810

8*f(6/5) - 4*f(1/2) = 270

16*f(5/3) - 8*f(6/5) = 1296

32*f(9/4) - 16*f(5/3) = 3600

64*f(4) - 32*f(9/4) = 9720

Adding all of these together cancels out all of the f() terms except for f(4):

63*f(4) = 14616

Therefore:

f(4) = 232