For the function y=x/(2x^2-3x-2), how to tell what is the domain of function? 

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain of a function consists of the values of x that yield a real values of f(x).

Here the function is: y = x/(2x^2-3x-2)

y = x/(2x^2-3x-2) does not yield real values if the denominator is equal to 0.

Solving 2x^2-3x-2 = 0

=> 2x^2 - 4x + x - 2 = 0

=> 2x(x - 2) + 1(x - 2) = 0

=> (2x + 1)(x - 2) = 0

x = -1/2 and x = 2

The domain of the given function is R - {-1/2, 2}

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll recall the definition of the domain of the function. The domain of the function comprises all the values of variable x that makes the expression of the function to exist.

In this case, the expression of the function is a fraction. The important condition for a fraction to be possible is that the denominator not to be zero value.

We'll check what are the x values that cancel the denominator. Simce the denominator is a quadratic, we'll apply quadratic formula:

x1 = [3+sqrt(9+16)]/4

x1 = (3+5)/4

x1 = 2

x2 = (3-5)/4

x2 = -1/2

The domain of definition of the given function is the real numbers set, except the values {-1/2 ; 2}, that cancel the denominator.

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