Final answer:
All given values of x have an image for the polynomial function f(x)=x³-20-3, as polynomials are defined for all real numbers and thus every real number is within their domain.
Step-by-step explanation:
The student's question asks for the value of x that would not have an image for the function f(x)=x³-20-3. Every function has an image for a real number within its domain unless the function is undefined for that number. In the case of a polynomial, every real number is within the domain, meaning every value of x will have an image. The function given is a polynomial, so it is defined for all real numbers, which means all the options A (x=2), B (x=3), C (x=5), and D (x=-4) will have an image. Therefore, there is no value of x among the given options that has no image for the function.