What is the domain and range of #f(x) = sqrt( x+3)#?

1 Answer
Apr 6, 2016

Answer:

Domain: #x in [-3,+oo)#
Range: #f(x) in [0,+oo)#

Explanation:

Assuming we are limited to Real numbers:

The argument of the square root operation must be #>=0#
therefore
#color(white)("XXX")x+3 >= 0 rarr x >= -3#

The square root operation provides a (primary) value which is non-negative.
As #xrarr +oo, sqrt(x+3)rarr +oo#
So the range of #f(x)# is #0# to #+oo#