Question:
The function f(x) = 2x - \(|x - x^2|\) is
The function f(x) = 2x - \(|x - x^2|\) is
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Absolute value functions $|g(x)|$ are continuous wherever $g(x)$ is continuous.
Updated On: Apr 30, 2026
- continuous at x = 1
- discontinuous at x = 1
- not defined at x = 1
- discontinuous at x = 0
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Sum of two continuous functions is continuous.
Step 2: Analysis
$2x$ is a polynomial (always continuous).
$|x - x^2|$ is a composite of absolute value and polynomial (always continuous).
Step 3: Test at x = 1
$f(1) = 2(1) - |1 - 1^2| = 2$.
LHL and RHL will also be 2 as the absolute value function is continuous everywhere.
Step 4: Conclusion
The function is continuous at $x=1$.
Final Answer:(A)
Sum of two continuous functions is continuous.
Step 2: Analysis
$2x$ is a polynomial (always continuous).
$|x - x^2|$ is a composite of absolute value and polynomial (always continuous).
Step 3: Test at x = 1
$f(1) = 2(1) - |1 - 1^2| = 2$.
LHL and RHL will also be 2 as the absolute value function is continuous everywhere.
Step 4: Conclusion
The function is continuous at $x=1$.
Final Answer:(A)
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