The main task is to find the quotient of two polynomial functions i(x) and j(x), but due to a potential typo in j(x), we cannot perform this calculation accurately. Upon correction, we would simplify the resulting function f(x) and evaluate it for specific x values, exploring the concept of dividing one function by another.
The question involves finding the quotient of two polynomial functions i(x) = 2x³ - x² - 13x + 1 and j(x) = 2x² + 32 - 5. To find this quotient, we would typically perform polynomial long division or synthetic division. However, without the correct expression for the divisor j(x), as the given function seems to have a typo, it is impossible to provide an accurate answer. If the correct function j(x) were given, the quotient would be another function, which we would denote as f(x). After obtaining f(x), we can simplify the expression accordingly.
Assuming the typo is corrected and we find the quotient function f(x), to evaluate it for specific values of x, we simply substitute the value of x into the simplified function f(x) and calculate the result. The concept of function quotients is similar to division of numbers but applied to functions, and represents how many times one function can 'fit into' another when the variable takes on specific values.