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What is the domain and range of # y =sqrt(2x - 3)#?

Answer 1

Domain : # x >=1.5 = [1.5, oo)#
Range : # {y : y > 0} =[0, oo) #

Domain (Possible values of x) is #(2x-3)>=0 or 2x >= 3 or x >= 3/2 or x >=1.5 = [1.5, oo)# Range ( value of y) is #{y : y > 0} =[0, oo)#. graph{(2x-3)^0.5 [-10, 10, -5, 5]} [Ans]

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Answer 2

Ethan Adkins

The domain of the function ( y = \sqrt{2x - 3} ) is all real numbers ( x ) such that the expression inside the square root, ( 2x - 3 ), is non-negative. This means:

[ 2x - 3 \geq 0 ]

Solving for ( x ):

[ 2x \geq 3 ]

[ x \geq \frac{3}{2} ]

So, the domain is ( x \geq \frac{3}{2} ).

The range of the function ( y = \sqrt{2x - 3} ) is all real numbers ( y ) such that ( y \geq 0 ), since the square root function outputs non-negative values.

Therefore, the domain is ( x \geq \frac{3}{2} ) and the range is ( 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.