The statement "g(x) = x^3 - 4x^2 + x + 6" represents a mathematical function where x is the variable. The function is defined such that for any value of x, the function g(x) will be the result of the operation x³ - 4x² + x + 6.
In this context, the expression "True" or "False" seems to connote the validity of the function. It is important to note that a mathematical function is simply a relationship between two sets, the 'domain' (in this case represented by the variable x) and the 'range' (the results g(x)). For any value of x that you can put into the function g(x) = x³ - 4x² + x + 6, there will always be a valid output or result, hence the function is valid.
Therefore, the answer is "True". This function "g(x) = x^3 - 4x^2 + x + 6" is valid as it can process any real number (as an input for x) and give a correspondingly real number as its output. This satisfies the definition of a valid mathematical function, thereby making the "True" the correct truth value for the function's validity.