F(x)=f(-x)

Solution for F(x)=f(-x) equation:

Simplifying
F(x) = f(-1x)

Multiply F * x
xF = f(-1x)

Remove parenthesis around (-1x)
xF = f * -1x

Reorder the terms for easier multiplication:
xF = -1f * x

Multiply f * x
xF = -1fx

Solving
xF = -1fx

Solving for variable 'x'.

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

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

Combine like terms: -1fx + fx = 0
fx + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(f + F) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(f + F)' equal to zero and attempt to solve:

Simplifying
f + F = 0

Reorder the terms:
F + f = 0

Solving
F + f = 0

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

Add '-1F' to each side of the equation.
F + -1F + f = 0 + -1F

Combine like terms: F + -1F = 0
0 + f = 0 + -1F
f = 0 + -1F
Remove the zero:
f = -1F

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

Combine like terms: f + -1f = 0
0 = -1F + -1f

Simplifying
0 = -1F + -1f

The solution to this equation could not be determined.

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