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

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

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

Reorder the terms:
f(1 + n) = 2f(n + -1)
(1 * f + n * f) = 2f(n + -1)
(1f + fn) = 2f(n + -1)

Reorder the terms:
1f + fn = 2f(-1 + n)
1f + fn = (-1 * 2f + n * 2f)
1f + fn = (-2f + 2fn)

Solving
1f + fn = -2f + 2fn

Solving for variable 'f'.

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

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

Combine like terms: 1f + 2f = 3f
3f + fn = -2f + 2f + 2fn

Combine like terms: -2f + 2f = 0
3f + fn = 0 + 2fn
3f + fn = 2fn

Add '-2fn' to each side of the equation.
3f + fn + -2fn = 2fn + -2fn

Combine like terms: fn + -2fn = -1fn
3f + -1fn = 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
3f + -1fn = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(3 + -1n) = 0

Subproblem 1
Set the factor 'f' equal to zero and attempt to solve:

Simplifying
f = 0

Solving
f = 0

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

Simplifying
f = 0
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Add 'n' to each side of the equation.
-1n + n = -3 + n

Combine like terms: -1n + n = 0
0 = -3 + n

Simplifying
0 = -3 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
f = {0}