Question

Domain ,range and co-domain of x^3

Answer 1

For the function f(x) = x³, we can determine its domain, range, and co-domain as follows:

1. Domain:
   The domain refers to the set of all possible values of x for which the function is defined. Since there are no restrictions on x (you can cube any real number), the domain is:

   Domain of f(x) = R (all real numbers)

2. Range:
   The range refers to the set of all possible values of f(x) (the outputs). Since the cubic function is continuous and can produce both positive and negative values for all real numbers, the range is also all real numbers:

   Range of f(x) = R

3. Co-domain:
   The co-domain is the set of possible values that the function could output, which is typically given in the context of the function's definition. In this case, if we're dealing with real numbers, the co-domain is also often taken as R:

   Co-domain of f(x) = R

Thus, for the function f(x) = x³:

• Domain: {R} (all real numbers)
• Range: {R} (all real numbers)
• Co-domain: {R} (all real numbers)