Find the domain of the function gx 4x74x2 9x9 SolutionGiven

Find the domain of the function g(x)= 4x+7/4x^2 -9x-9

Given that

g(x) = ( 4x + 7 ) / ( 4x² - 9x - 9 )

We know that

The domain of function is the set of input values for which the function is real and defined

Set denominator of given function equal to zero for finding undefined value x

4x² - 9x - 9 = 0

( x - 3 ) (4x + 3 ) = 0

x - 3 = 0 , 4x + 3 = 0

x = 3 , 4x = -3

x = -3/4

The function domain is ,

x < -3/4 or -3/4 < x < 3 or x > 3