Let the function f be defined by the equation y=f(x), where x and f(x) are real numbers. Find the domain of the function f(x)= 'squareroot' 16x^2-4)

Find the domain of  y  =  sqrt( 16x² - 4 ).

 

The domain consists of all the values of x that will make the function defined. In this case, all the values of x that result in the expression  16x² - 4  >=  0.

 

To solve:  16x² - 4  >=  0

 

Divide all terms by 4:  4x² - 1  >=  0

--->                                   4x²  >=  1

--->                                     x²  >=  1/4

Find the square root of both sides and divide into two inequalities:

--->                     Either  x <= -1/2    or   x >= 1/2

 

Answer:      ( -infinity, -1/2 )  union  ( 1/2, infinity )