Determine the value of ' \( k \) ' for which the following function is continuous at \( x=3 \) : (CBSE 2017) \[ f(x)=\left\{\begin{array}{cc} \frac{(x+3)^{2}-36}{x-3} & , x \neq 3 \\ k & , x=3 \end{array}\right. \]

Question

Determine the value of ' \( k \) ' for which the following function is continuous at \( x=3 \) : (CBSE 2017) \[ f(x)=\left\{\begin{array}{cc} \frac{(x+3)^{2}-36}{x-3} & , x \neq 3 \\ k & , x=3 \end{array}\right. \]

Answer 1

Given that, f(x) is continuous at x=3

Thus, f ( x ) is continuous at x = 3 , if k = 12 .