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If: x = -3x+1
Then: x+3x = 1 => 4x =1
So: x = 1/4 or 0.25
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I notice that the question requests a solution for g x = -3x + 1.
It seems possible that parentheses around the 'x' after the 'g' have gone missing, along with a prime indicating the derivative of the function g. This being the case, we would be seeking the antiderivative of -3x + 1.
The antiderivative of a sum is the sum of the antiderivatives. So we can look at -3x and +1 separately.
The derivative of x2 is 2x. Therefore, the antiderivative of x is x2/2, and the antiderivative of -3x is -3x2/2.
The antiderivative of 1 is x.
Overall, the solution is the antiderivative -3x2/2 + x + C, where C is an arbitrary constant.
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