f(1)=-2f(1-1)+1

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

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

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

Combine like terms: 1 + -1 = 0
1f = -2f(0) + 1

Reorder the terms for easier multiplication:
1f = -2 * 0f + 1

Multiply -2 * 0
1f = 0f + 1

Anything times zero is zero.
1f = 0f + 1

Combine like terms: 0 + 1 = 1
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