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)#