Question

Which statement describes the domain of the function f(x) = 3x/[(4x^2) −4] ?

Option 1: All real numbers
Option 2: All nonzero real numbers
Option 3: All real numbers except x= 3/4
Option 4: All real numbers except x=−1 and x=1

Answer 1

The domain of the function f(x) = 3x/[(4x^2) −4] is all real numbers except x = -1 and x = 1, where the denominator is zero and the function undefined.

Step-by-step explanation:

The function in question is f(x) = 3x/[(4x^2) −4]. To determine its domain, we must identify the values of x for which the function is not defined. In this case, the denominator cannot be zero because division by zero is undefined. Thus, we set the denominator equal to zero and solve for x:

(4x^2) - 4 = 0

4x^2 = 4

x^2 = 1

x = ±1

Therefore, the domain of the function is all real numbers except x = -1 and x = 1, because at these points the denominator becomes zero, making the function undefined. The correct option is Option 4.