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# 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.  Expanding using the formula: (a + b)2 = a2 + b+ 2ab  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.

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