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

Jun 4, 2017

Consider the function,

$f \left(x\right) = {x}^{2} + 5$

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

For $f \left(x\right)$ to be real valued, all real values of $x$ are consistent with the definition of $f \left(x\right)$.

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 $x$, $f \left(x\right)$ varies from $5$ to infinity.

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