Find the domain of (g(x) = frac{4x^{2} – 1}{sqrt{9x^{2} + 1}})
-
A.
({x : x in R, x = frac{1}{2}}) -
B.
(x: x in R, xneq frac{1}{3}) -
C.
(x : x in R, x = frac{1}{3}) -
D.
(x: x in R)
Correct Answer: Option D
Explanation
The domain of a function refers to the regions where the function is defined or has a value on a particular region.
(frac{4x^{2} – 1}{sqrt{9x^{2} + 1}}) has a domain defined on all set of real numbers because the function is defined on the set of real numbers when the denominator (sqrt{9x^{2} + 1} geq 0).
(sqrt{9x^{2} + 1} geq 0 implies 9x^{2} + 1 geq 0) which because of the square sign has a value for all values of x, be it negative or positive.