If f(x), defined by \(f(x)=\begin{cases}kx+1 & \text{if } x \le \pi\\ \cos x & \text{if } x \gt \pi\end{cases}\) is continuous at \(x=\pi\), then the value of k is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(-\displaystyle\frac{2}{\pi}\)
For continuity at x = π, the value at π must equal the right-hand limit (the left-hand limit comes from the same piece kx + 1).
\(f(\pi) = k\pi + 1\)
\( \displaystyle \lim_{x \to \pi^{+}} f(x) = \cos\pi = -1 \)
Equating:
\(k\pi + 1 = -1\)
\(k\pi = -2\)
\( \displaystyle k = -\frac{2}{\pi} \)
NCERT (2026-27 edition):
Continuity
