Final answer:
The domain of f(x)=x−2/(1x^3−3x+1) will be all real numbers except for any values that make the denominator of the fraction 1x^3−3x+1 equal to zero. These values can be found by solving the equation 1x^3−3x+1=0.
Step-by-step explanation:
The function given is f(x)=x−2/(1x^3−3x+1). The domain of a function is the set of all real numbers for which the function is defined. For this function, it is defined for all values of x except for those that would make the denominator of the fraction zero since division by zero is undefined in mathematics. To find these exceptions, we must solve the equation 1x^3−3x+1=0. Unfortunately, this polynomial is not easily factorable, so we may need to use graphing or a numerical method to find the solutions. These solutions are the values that x cannot be. Thus, the domain of f will be all real numbers except for the solutions to the equation 1x^3 - 3x + 1 = 0.
Learn more about Domain of a Function