Question

What is the domain and range of `f(x) = x^2 + 5`?

Answer 1

Consider the function,

`f(x) = x^2 + 5`

The domain is the set of all possible values of `x` for which this function is defined.

For `f(x)` to be real valued, all real values of `x` are consistent with the definition of `f(x)`.

Thus, domain is `R`, the set of real numbers.

The range in this case is also `R` since it is a real valued function.

Another thing that might be added is that the codomain which is the set of values in the range `R` to which elements of the domain are mapped.

Well, for any value of `x`, `f(x)` varies from `5` to infinity.

Thus, codomain, extends from `5` to infinity.