Question

The number of point / points where the function \(f(x) = \frac{1}{x^2-5|x|+6}\) is discontinuous is......

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(4\)

Hint:

The function is discontinuous where the denominator is zero.

Answer 1

The Correct Option is D

Step 1: Solve the denominator:
$|x| = 2 \Rightarrow x = 2, -2$ and $|x| = 3 \Rightarrow x = 3, -3$.

Step 2: Count:
Four values make the denominator vanish and the function is undefined and discontinuous there.

Final Answer:
The count is $4$, option (D). \[ \boxed{4} \]