f(n)=2f(n-2)

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


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

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

Reorder the terms:
fn = 2f(-2 + n)
fn = (-2 * 2f + n * 2f)
fn = (-4f + 2fn)

Solving
fn = -4f + 2fn

Solving for variable 'f'.

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

Add '4f' to each side of the equation.
4f + fn = -4f + 4f + 2fn

Combine like terms: -4f + 4f = 0
4f + fn = 0 + 2fn
4f + fn = 2fn

Add '-2fn' to each side of the equation.
4f + fn + -2fn = 2fn + -2fn

Combine like terms: fn + -2fn = -1fn
4f + -1fn = 2fn + -2fn

Combine like terms: 2fn + -2fn = 0
4f + -1fn = 0

Factor out the Greatest Common Factor (GCF), 'f'.
f(4 + -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 '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Add 'n' to each side of the equation.
-1n + n = -4 + n

Combine like terms: -1n + n = 0
0 = -4 + n

Simplifying
0 = -4 + 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}

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