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

Answer 1

Kennedy Adams

#x in RR,x>=-5#

#"the expression inside the radical must be greater than"# #"or equal to zero"#

#"solve "x+5>=0" for domain"#

#"subtract 5 from both sides"#

#xcancel(+5)cancel(-5)>=0-5#

#rArrx>=-5#

#"domain is "x in RR,x>=-5#

#[-5,+oo)larrcolor(blue)"in interval notation"# graph{sqrt(x+5) [-10, 10, -5, 5]}

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Answer 2

Abigail Allen

To find the domain of ( \sqrt{x + 5} ), the expression inside the square root must be greater than or equal to zero. So, ( x + 5 \geq 0 ). Solving for ( x ), we get ( x \geq -5 ). Therefore, the domain of ( \sqrt{x + 5} ) is all real numbers greater than or equal to -5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.