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

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Answer 1 · 2017-06-04T14:56:18

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.

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