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Question #40342

Difficulty: 8/10 | 🟢 Free

The Question

Let $S$ be the set of all integers in the domain of the real-valued function $f(x) = \frac{\sqrt{25 - x^2}}{\ln(|x^3 - 3x^2 - 4x + 12|)} + \ln(|x^2 - x - 2|)$ . Find the sum of all elements in $S$ .

Options

A.
-2
B.
0
C.
9
D.
-3

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Bridge

Practice problems that bridge the gap between foundational theory and advanced practical application.

Concepts Behind This Question

Real-Valued Function Domain|Logarithmic Differentiation Domain|Modulus Function Breakdown

Why This Question Is Tricky

Common Mistakes

This question tests the domain constraints of logarithmic functions composed with absolute values.

A common trap is assuming that since $|g(x)| \ge 0$ , the domain of $\ln(|g(x)|)$ is all real numbers.

Students must explicitly exclude the roots of $g(x)$ where the argument becomes zero.

Furthermore, it filters out students who incorrectly solve $g(x) > 0$ instead of $g(x) \neq 0$ , confusing the domain of $\ln(g(x))$ with $\ln(|g(x)|)$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Relations and Functions - Class 11
Concept	Real-Valued Function Domain
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free