g(x)=5x^2/8x^2-2x-3

Question

find the domain of g(x)

Answer 1

g(x) = 5x² / (8x² - 2x - 3)

 

 

The domain is the values of x where g(x) is defined.  In order to find the domain, we set the denominator of g(x) equal to zero because dividing by zero makes the function undefined.

 

8x² - 2x - 3 = 0

 

(4x - 3)(2x + 1) = 0

 

Set the factors equal to zero.

 

4x - 3 = 0                  2x + 1 = 0

4x = 3                       2x = -1

 

x = 3/4                        x = -1/2

 

The function is undefined at these x values.

 

The domain is

 

(-∞, -1/2)∪(-1/2, 3/4)∪(3/4, ∞)