(F*g)(x)=f(g(x))

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Solution for (F*g)(x)=f(g(x)) equation: 


Simplifying
(F * g)(x) = f(g(x))

Multiply F * g
(gF)(x) = f(g(x))

Multiply gF * x
gxF = f(g(x))

Multiply g * x
gxF = f(gx)

Multiply f * gx
gxF = fgx

Solving
gxF = fgx

Solving for variable 'g'.

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

Add '-1fgx' to each side of the equation.
-1fgx + gxF = fgx + -1fgx

Combine like terms: fgx + -1fgx = 0
-1fgx + gxF = 0

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


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

Simplifying
gx = 0

Solving
gx = 0

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

Simplifying
gx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1f + F)' equal to zero and attempt to solve:

Simplifying
-1f + F = 0

Reorder the terms:
F + -1f = 0

Solving
F + -1f = 0

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

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

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

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

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

Simplifying
0 = -1F + f

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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