Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
FURTHER MATHEMATICS
WAEC 2018
Find the domain of \(g(x) = \frac{4x^{2} - 1}{\sqrt{9x^{2} + 1}}\)
- A. \({x : x \in R, x = \frac{1}{2}}\)
- B. \(x: x \in R, x\neq \frac{1}{3}\)
- C. \(x : x \in R, x = \frac{1}{3}\)
- D. \(x: x \in R\)
Correct Answer: D. \(x: x \in R\)
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.
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *