Determine the value of ‘k’ for which the following function is continuous at x = 3:

  (CBSE 2017)

Since f(x) is continuous at x = 3.

Now, factorizing (x² + 6x - 27) such that the product is 27 and difference is 6, we get,

(x² + 6x - 27) = x² + 9x - 3x - 27 = x(x + 9) - 3(x + 9)

(x² + 6x - 27) = (x -3) (x + 9)

Therefore,

⇒ 12 = k

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