Question

domain and rangr of y=x/(2-3x)

Answer 1

Answer:

y= (-1/3, infinity) ; for x<2/3. increasing curve

y= (-infinity, -1/3) ; for x>2/3. increasing curve

y= undefined ; for x=2/3.

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Explanation:

First let's try to find out the locally maximum and/or minimum value of y.

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If 2-3x=0, then x= 2/3 = 0.667.

therefore, y is infinity at x=0.667.

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Thus, y is an increasing function and lies between -1/3 and infinity, for the domain x< 2/3, i.e. for all values of x between (-infinity, 2/3).

For x= -infinity, by limits, we get y= -1/3.

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Now, let's see the scenario for domain x > 2/3.

if x= infinity, then by L'Hopital's rule on limits, we get,

y= lim (x -> infinity) x/(2-3x) = -1/3 = -0.333

-0.333 is the local maximum value of y.

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So y is an increasing fuction and lies between -infinity and -1/3, for the domain x > 2/3.