f(x)*f(-x)=f(x)+f(-x)

Solution for f(x)*f(-x)=f(x)+f(-x) equation:

Simplifying
f(x) * f(-1x) = f(x) + f(-1x)

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

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

Multiply f * x
-1fx * f * x = f(x) + f(-1x)

Multiply fx * f
-1f2x * x = f(x) + f(-1x)

Multiply f2x * x
-1f2x2 = f(x) + f(-1x)

Multiply f * x
-1f2x2 = fx + f(-1x)

Remove parenthesis around (-1x)
-1f2x2 = fx + f * -1x

Reorder the terms for easier multiplication:
-1f2x2 = fx + -1f * x

Multiply f * x
-1f2x2 = fx + -1fx

Combine like terms: fx + -1fx = 0
-1f2x2 = 0

Solving
-1f2x2 = 0

Solving for variable 'f'.

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

Divide each side by '-1'.
f2x2 = 0

Simplifying
f2x2 = 0

The solution to this equation could not be determined.