f(2x+1)=f(2x)+1

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

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

Reorder the terms:
f(1 + 2x) = f(2x) + 1
(1 * f + 2x * f) = f(2x) + 1
(1f + 2fx) = f(2x) + 1

Remove parenthesis around (2x)
1f + 2fx = f * 2x + 1

Reorder the terms for easier multiplication:
1f + 2fx = 2f * x + 1

Multiply f * x
1f + 2fx = 2fx + 1

Reorder the terms:
1f + 2fx = 1 + 2fx

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

Combine like terms: 2fx + -2fx = 0
1f + 0 = 1 + 2fx + -2fx
1f = 1 + 2fx + -2fx

Combine like terms: 2fx + -2fx = 0
1f = 1 + 0
1f = 1

Solving
1f = 1

Solving for variable 'f'.

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

Divide each side by '1'.
f = 1

Simplifying
f = 1