Q94 / 180 · KCET 2015 · Mathematics

\( f(x)=\left\{\begin{array}{cl}3 x-8 & \text { if } x \leq 5 \\ 2 k & \text { if } x>5\end{array}\right. \) is continuous, find \( k . \)

  • A
    \( \frac{2}{7} \)
  • B
    \( \frac{3}{7} \)
  • C
    \( \frac{4}{7} \)
  • Correct answer
    D
    \( \frac{7}{2} \)

Solution

Given that, $f(x)=\left\{\begin{array}{cc}3 x-8 & x \leq 5 \\ 2 k & x>5\end{array}\right.$ At $x=5$, we have $f(5)=3(5)-8=7$ Taking R.H.L, we have $\lim _{x \rightarrow 5} 2 k=2 k$ $\mathrm{WE}$ know that for continuous L.H.L $=$ R.H.L. Therefore, $7=2 k \Rightarrow k=\frac{7}{2}$

Hence, the correct answer is option: 'D'.

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