f(2n)=f(n)+1

Solution for f(2n)=f(n)+1 equation:

Simplifying
f(2n) = f(n) + 1

Remove parenthesis around (2n)
f * 2n = f(n) + 1

Reorder the terms for easier multiplication:
2f * n = f(n) + 1

Multiply f * n
2fn = f(n) + 1

Multiply f * n
2fn = fn + 1

Reorder the terms:
2fn = 1 + fn

Solving
2fn = 1 + fn

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Add '-1fn' to each side of the equation.
2fn + -1fn = 1 + fn + -1fn

Combine like terms: 2fn + -1fn = 1fn
1fn = 1 + fn + -1fn

Combine like terms: fn + -1fn = 0
1fn = 1 + 0
1fn = 1

Divide each side by '1n'.
f = n-1

Simplifying
f = n-1