f(n)=3f(n-1)

Solution for f(n)=3f(n-1) equation:

Simplifying
f(n) = 3f(n + -1)

Multiply f * n
fn = 3f(n + -1)

Reorder the terms:
fn = 3f(-1 + n)
fn = (-1 * 3f + n * 3f)
fn = (-3f + 3fn)

Solving
fn = -3f + 3fn

Solving for variable 'f'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'f'.
f(3 + -2n) = 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 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

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

Combine like terms: -2n + 2n = 0
0 = -3 + 2n

Simplifying
0 = -3 + 2n

The solution to this equation could not be determined.

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