How do you find the domain and range of #g(x) = sqrt(x-4) #?

Answer 1

Eli Assouline

Domain : #x>=4 or [4,oo)#
Range : #g(x)>=0 or [0,oo)#

#g(x)=sqrt(x-4); g(x)# is undefined at #x<4:. x>=4#

Hence domain is #x>=4 or [4,oo)#

Range: Output of square root is #>=0:. g(x)>=0#

Hence range is #g(x)>=0 or [0,oo)#

graph{(x-4)^0.5 [–20,–20,–10]} [Ans]

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Answer 2

Eva Abramson

To find the domain of ( g(x) = \sqrt{x-4} ), set the expression inside the square root greater than or equal to zero and solve for ( x ). The domain is ( x \geq 4 ). The range is all real numbers greater than or equal to 0, denoted as ( y \geq 0 ).

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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.