Question:
The number of points at which the function \( f(x)=\frac{1{\log_e|x|} \) is discontinuous is}
The number of points at which the function \( f(x)=\frac{1{\log_e|x|} \) is discontinuous is}
Show Hint
Always check both domain restrictions and denominator zeros for discontinuities.
Updated On: May 8, 2026
- 1
- 2
- 3
- 4
- infinitely many
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Function is undefined when:
\[
\log|x| = 0 \quad \text{or} \quad |x| \le 0
\]
Step 1: Domain condition
\[ |x| > 0 \Rightarrow x \ne 0 \] So discontinuity at: \[ x=0 \]
Step 2: Solve denominator zero
\[ \log|x|=0 \Rightarrow |x|=1 \] \[ x = \pm 1 \]
Step 3: Identify discontinuities
Points: \[ x=0, 1, -1 \]
Step 4: Total count
\[ 3 \text{ points} \]
Step 5: Final Answer
\[ \boxed{3} \]
Step 1: Domain condition
\[ |x| > 0 \Rightarrow x \ne 0 \] So discontinuity at: \[ x=0 \]
Step 2: Solve denominator zero
\[ \log|x|=0 \Rightarrow |x|=1 \] \[ x = \pm 1 \]
Step 3: Identify discontinuities
Points: \[ x=0, 1, -1 \]
Step 4: Total count
\[ 3 \text{ points} \]
Step 5: Final Answer
\[ \boxed{3} \]
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