WAEC Further Mathematics 2018 Paper

Concept:The domain is the set of all real $x$ for which the expression is defined.Explanation:The function is $g(x) = \dfrac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}$.For the denominator to be defined and non-zero, we need $9x^{2} + 1 > 0$.Since $x^2 \ge 0$, we have $9x^2 + 1 \ge 1 > 0$ for every real $x$.Thus the square root is always real and never zero.The numerator is a polynomial, which is also defined for all real $x$.Therefore $g(x)$ is defined for every real number.Answer:Domain $= \{x : x \in \mathbb{R}\}$, which is option D.