f(x)=cos^2(3x^4+1)

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Solution for f(x)=cos^2(3x^4+1) equation: 


Simplifying
f(x) = cos2(3x4 + 1)

Multiply f * x
fx = cos2(3x4 + 1)

Reorder the terms:
fx = cos2(1 + 3x4)
fx = (1 * cos2 + 3x4 * cos2)
fx = (1cos2 + 3cos2x4)

Solving
fx = 1cos2 + 3cos2x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = cos2x-1 + 3cos2x3

Simplifying
f = cos2x-1 + 3cos2x3

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