How do you find the domain and range of $f(x) = x^2 + 5$ ?

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Answer 1 · 2017-05-21T12:15:09

Domain: $(-oo,+oo)$
Range: $[5,+oo)$

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

$f(x)$ is defined $forall x in RR$

Hence, the domain of $f(x)$ is $(-oo,+oo)$

$f(x)$ is a parabola and hence has a single critical value.

Since the coefficient of $x^2$ is positive, $f(x)$ has an absolute minimum value and no upper bound.

Since $x^2 >=0 forall x in RR -> f(x)_"min" = f(0)$

$:. f(x)_"min" = 5$

Hence, the range of $f(x)$ is $[5,+oo)$

How do you find the domain and range of f(x) = x^2 + 5f(x) = x^2 + 5?