If the function \(f(x) = \begin{cases} 3x - 8 & \text{if } x \le 5\\ 2\mathrm{K} & \text{if } x \gt 5\end{cases}\) is continuous, then the value of K is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{7}{2}\)
Each piece is continuous on its own, so the only point to check is x = 5, where the formula changes. f is continuous at x = 5 when the left-hand limit, the right-hand limit and f(5) are equal.
\(f(5) = 3(5) - 8 = 7\)
\(\text{LHL} = 3(5) - 8 = 7\)
\(\text{RHL} = 2\mathrm{K}\)
Equating:
\(2\mathrm{K} = 7\)
\( \displaystyle \mathrm{K} = \frac{7}{2} \)