suppose g(x) = 1 / √(25 - x²). what is the largest interval on which g(x) is continuous? enter your answer…
suppose g(x) = 1 / √(25 - x²). what is the largest interval on which g(x) is continuous? enter your answer in interval notation interval
Answer
Explanation:
Step1: Determine domain for continuity
For $g(x)=\frac{1}{\sqrt{25 - x^{2}}}$ to be continuous, the denominator $\sqrt{25 - x^{2}}\neq0$ and $25 - x^{2}>0$.
Step2: Solve the inequality
Solve $25 - x^{2}>0$. Rewrite it as $x^{2}<25$, so $- 5<x<5$.
Answer:
$(-5,5)$