Question:
If the function \(f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}\) is continuous at x = 5, then the value of a - b is :-
If the function \(f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}\) is continuous at x = 5, then the value of a - b is :-
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Equate left and right limits at x=5; note pi is about 3.14, so |pi-5| = 5-pi.
Updated On: Nov 5, 2026
- \(\frac{2}{\pi - 5}\)
- \(\frac{2}{5 - \pi}\)
- \(\frac{-2}{\pi + 5}\)
- \(\frac{2}{\pi + 5}\)
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The Correct Option is B
Solution and Explanation
Left limit at 5: \(a|\pi-5| + 1 = a(5-\pi) + 1\) (since \(\pi\lt5\)).
Right limit at 5: \(b|5-\pi| + 3 = b(5-\pi) + 3\).
Continuity: \(a(5-\pi) + 1 = b(5-\pi) + 3 \Rightarrow (a-b)(5-\pi) = 2\).
\(a - b = \frac{2}{5-\pi}\).
Answer: (2) \(\frac{2}{5-\pi}\)
Right limit at 5: \(b|5-\pi| + 3 = b(5-\pi) + 3\).
Continuity: \(a(5-\pi) + 1 = b(5-\pi) + 3 \Rightarrow (a-b)(5-\pi) = 2\).
\(a - b = \frac{2}{5-\pi}\).
Answer: (2) \(\frac{2}{5-\pi}\)
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