How do you find the domain and range of #f(x) = sqrt(x+3)#?

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Answer 1 · 2017-09-11T23:03:12

See below.

This is for positive roots, since #sqrt(a)# usually implies positive roots.

For real numbers #x + 3 >= 0 => x >= -3#

So domain is:

#{x in RR | x>= -3 }#

Minimum value of range is #0# when #x = -3#

#sqrt( -3 + 3 ) = 0#

As #x -> oo#

#sqrt(x + 3) -> oo#

so range is:

#{y in RR | y >= 0 }#