How do you find the domain and range of #sqrt(x+5)#?

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Answer 1 · 2017-05-18T18:25:40

Domain#: {x in RR | x geq - 5}#

Range#: {f(x) in RR | f(x) geq 0}#

We have: #f(x) = sqrt(x + 5)#

The domain of any square root function is dependent on its argument.

The argument must be greater than or equal to zero:

#Rightarrow x + 5 geq 0#

#Rightarrow x geq - 5#

The square root function never produces a negative result.

So the range will be greater than or equal to zero as well:

#Rightarrow f(x) geq 0#

Therefore, for the function #f(x) = sqrt(x + 5)#, the domain is #{x in RR | x geq - 5}# and the range is #{f(x) in RR | f(x) geq 0}#.