Find the domain of the curve y=x/(2x-3)^2. 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The domain of a function y = f(x) is all values of x for which y is a real number.

Here we have y = x / (2x - 3)^2

y is defined for all values of x except when 2x - 3 = 0. The result of a number divided by 0 is not defined as a real number.

The required domain does not contain 2x - 3 = 0

=> x = 3/2

The domain of the function y = x / (2x - 3)^2 = {R} - (3/2)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the curve y= x/ (2x-3)^2

The domain is all x values such that the function is defined.

Since the function is a ratio, then the denominator should NOT be zero.

Let us determine the zeros of the denominator.

==> 2x-3 = 0 ==> 2x = 3 ==> x = 3/2

Then the domain is all x values except 3/2.

==> The domain = R - { 3/2 }

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